The author of Genesis is generally considered to be Moses.
From the article "In the Beginning God" By Dr. Hal Harless
"{Norman} Geisler explains the lines of evidence for this conclusion:
There are several lines of evidence to indicate that Moses, the
great lawgiver and deliverer of Israel who wrote the other four books of the
law, was the author of Genesis. (1) The earliest and continual tradition of
'the Jewish people, as recorded in the Talmud, attributes this book to
Moses. (2) Moses is the only person we know of from this early time peri
od who had the ability to write this book. The rest of the Israelites were a
nation of uneducated slaves, whereas Moses was a highly educated son
of the king (Acts 7:22). (3) Moses was the only one who had both the in
terest and information to write Genesis. Being Jewish
Moses would havehad access to the family records of his ancestors (cf. Gen. 5:1; 10:1;
25:19; etc.) which were no doubt brought down to Egypt by Jacob (Gen.
46). Since Moses was bent on delivering his people from Egypt, it is nat
ural
to assume that he was familiar with the promises of God passed down
by his forefathers that God would indeed deliver them (cf. Gen. 46:3–4;
Exod. 2:24). (4) Citations from Genesis show that the rest of the Old Test
ament regards it as part of the Law of Moses (Deut. 1:8; II Kings 13:23; I
Chron. 1:1ff.). Since Moses was the author of the other "books of Moses,"
as we will see later,
it is reasonable to attribute the first book of Moses to
him as well..."
http://ffgreenville.org/notes/books/gen_2013/2013-01-27-gen-001-001.pdf
