Deuteronomy 34:1–12
Then Moses went up from the plains of Moab to Mount Nebo, to the top of Pisgah, which is across from Jericho. And the LORD showed him all the land of Gilead as far as Dan . . . . So Moses the servant of the LORD died there in the land of Moab, according to the word of the LORD. And He buried him in a valley in the land of Moab, opposite Beth Peor; but no one knows his grave to this day. Moses was one hundred and twenty years old when he died. His eyes were not dim nor his natural vigor diminished . . . .

Moses is considered the author of the first five books of the Bible; the Pentateuch (Deuteronomy 31:24). Liberal scholars have rejected this claim, and theories abound as to the “true” authorship. Despite the detractors, the life and death of Moses are contained within these books, along with the account of the creation of the universe and the calling of the chosen people through Abraham, Isaac, and Jacob (Israel).

After wandering through the wilderness following the Exodus, the Children of Israel are poised at the edge of the Promised Land. At this time, the authority of leadership held by Moses was transferred to Joshua (Deuteronomy 31:23). Joshua was to lead the nation into their new homeland without the company of Moses.

Deuteronomy 34:4
Then the LORD said to him, “This is the land of which I swore to give Abraham, Isaac, and Jacob, saying, ‘I will give it to your descendants.’ I have caused you to see it with your eyes, but you shall not cross over there.”

After having seen the Promised Land, Moses died and was buried by God (Deuteronomy 34:5–6). If Moses was dead, then how could he be considered the author of Deuteronomy?

At the time of the writing, books were contained on scrolls. The ending of one book and the beginning of the next were not clearly delineated. In modern translations there are many instances where the last verse is considered the first verse of the next chapter in the Jewish text. This does not mean that there is an error, but that the demarcations are different.

Likewise, the last chapter of Deuteronomy could as easily be considered the first chapter of Joshua without harming the integrity of the text. This is one possible solution to the inferred contradiction.

Another possibility is that, having recorded the final words of blessing in Deuteronomy 33:29, another writer completed the story of Moses after his death. Being divinely inspired (2 Timothy 3:16–17), the author noted these last activities of Moses and placed them in the records. Exactly who this author was is a matter of dispute. Whether Joshua, Ezra, Eliazar, or another, the account simply closes out the life of Moses.

Whether we should rearrange the chapters or ascribe a different author to that small portion, there is no contradiction in the text. No truth of Scripture is altered by either of these resolutions to the apparent problem. If, upon your death, someone were to take your journal or personal memoirs and add a short description of your death, you would still be considered the author of the biography.  http://www.answersingenesis.org/articles/2009/02/23/contradictions-dead-man-writing