Bible critics often say that Moses did not write the first five books of the Bible (the Pentateuch), but that it was written by several authors at a much later time. Perhaps in your college religion class, your professor told you that only naive people believe that Moses actually wrote any of the Bible, but now we modern scholars know better? The question is, do they really know this for a fact?
We’ve seen in a previous article that Archaeology shows writing existed in Moses’s time and confirms the antiquity of the Pentateuch. But there is plenty of other kinds of evidence that support Mosaic authorship.
First, throughout the Bible, different writers testify to Mosaic authorship. Some examples from the Old Testament: Exodus 17:14 “And the Lord said to Moses, write this for a memorial in a book”, Ex 24:4 “and Moses wrote all the words of the Lord”, Ex. 34:27 , Numbers 33:1-2, Deuteronomy 31:9″ And Moses wrote this law, and delivered it unto the priests.” Similar references occur in Joshua 8:32, 1 Kings 2:3, 2 Kings 14:6, , 21:8, Ezra 6:18, Nehemiah 13:1, Daniel 9:11-13, Malachi 4:4.
In the New Testament, Jesus referred to Moses’ authorship: John 5:46-47 “For if you believe Moses, you would believe me, for he wrote of me”, John 7:19 “Did not Moses give you the law?” Other New Testament references include Acts 3:22, Romans 10:5, Mark 12:26.
If the critics are right, then we would have to attribute error or falsehood to Christ, His apostles, and many of the Old Testament writers. I think if we don’t believe Jesus, we have bigger problems than whether or not Moses wrote the Pentateuch.
There are also other internal evidences. The text includes many Egyptian names and loan words . Also the seasons and crop sequence referred to such as in Exodus 9:31-32 better fit Egypt than Palestine. The animals and plants mentioned, such as the shittim or acacia tree (a desert tree) or the skins of the dugong,(tahash) an animal found in the seas next to Egypt and the Sinai ( see Exodus 25:5, 36:19), are native to the Egyptian area, not Palestine. And the geographical references seem to come from an Egyptian perspective. In Genesis 13:10, the writer compares the Jordan plain to “the land of Egypt as thou comest unto Zoar”, to give his Egyptian audience a picture they were familiar with. Also in Genesis 33:18, there is a reference to Shalem, “a city of Shechem, which is in the land of Canaan.” Why would it be necessary to tell them this city was in the land of Canaan when they had been living there for generations?  Finally, tents and other references show a nomadic desert setting, rather than an established agricultural setting. 
As a former member of the Egyptian court, Moses would have had all the education and qualifications for this writing task. The book of Deuteronomy, and parts of Exodus and Leviticus are in a form of a covenant treaty that can be shown to belong to the very time period that Moses lived in, and not before or after.  the evidence does not fit a later inventor writing in the time of Josiah or anytime in the first millenium B.C.E.
Kitchen comments: “So how come documents such as Exodus-Leviticus and Deuteronomy just happen to embody very closely the framework and order and much of the nature of the contents of such treaties and law collections established by kings and their scribal staffs…in the late second millenium?…To exploit such concepts and formats for his people’s use at that time, the Hebrew’s leader would necessarily had to have been in a position to know of such documents at first hand…we need a Hebrew leader who had experience of life at the Egyptian court, including knowledge of treaty-type documents and their format,as well as of traditional Semitic legal/social usage more familiar to his own folk. In other words, somebody distressingly like that old ‘hero’ of biblical tradition, Moses, is badly needed at this point…” 
Other reasons to support the writing of the Pentateuch to be in the time of Moses:
So the evidence points to Moses as the writer of the first five books of the Bible, the Pentateuch. (Note: as far as the book of Genesis goes, there is evidence that Moses used and compiled ancient records before his time to put it together, rather than directly writing the book as in Exodus through Deuteronomy. For an excellent article that shows how Moses could have written/compiled the Book of Genesis, see here.
I think we should listen to Jesus when He said that Moses wrote, instead of our religion professor who claims to know better 25 centuries later!
 Gleason Archer, A Survey of Old Testament Introduction, Moody Press, Chicago, IL, 1994, pp.118-121
 Ibid., pp. 121-122
 Ibid., pp. 122-123
 Kenneth Kitchen, On the Reliability of the Old Testament, Eerdmans Publishing Co., Grand Rapids, MI, 2003, pp. 283-295.
 Ibid., p. 295.