Since the question asked what Jehovah's Witnesses believed, here is a list of books and their writers. This information was taken from the 2013 revision of the New World Translation of the Holy Scriptures. The table is easier to read in the printed version than that link, so here is a link where you can download the PDF version. Right after Revelation you will see the Table of the Books of the Bible. I was tempted to only provide the links, but these answers a supposed to contain the answer in the text, not just links so I here it is. I thought it was more useful to keep it as a list of books with their writers than just writers.
- Genesis: Moses
- Exodus: Moses
- Leviticus: Moses
- Numbers: Moses
- Deuteronomy: Moses
- Joshua: Joshua
- Judges: Samuel
- Ruth: Samuel
- 1 Samuel: Samuel; Gad; Nathan
- 2 Samuel: Gad; Nathan
- 1 Kings: Jeremiah
- 2 Kings: Jeremiah
- 1 Chronicles: Ezra
- 2 Chronicles: Ezra
- Ezra: Ezra
- Nehemiah: Nehemiah
- Esther: Mordecai
- Job: Moses
- Psalms: David and others
- Proverbs: Solomon; Agur; Lemuel
- Ecclesiastes: Solomon
- Song of Solomon: Solomon
- Isaiah: Isaiah
- Jeremiah: Jeremiah
- Lamentations: Jeremiah
- Ezekiel: Ezekiel
- Daniel: Daniel
- Hosea: Hosea
- Joel: Joel
- Amos: Amos
- Obadiah: Obadiah
- Jonah: Jonah
- Micah: Micah
- Nahum: Nahum
- Habakkuk: Habakkuk
- Zephaniah: Zephaniah
- Haggai: Haggai
- Zechariah: Zechariah
- Malachi: Malachi
- Matthew: Matthew
- Mark: Mark
- Luke: Luke
- John: Apostle John
- Acts: Luke
- Romans: Paul
- 1 Corinthians: Paul
- 2 Corinthians: Paul
- Galatians: Paul
- Ephesians: Paul
- Philippians: Paul
- Colossians: Paul
- 1 Thessalonians: Paul
- 2 Thessalonians: Paul
- 1 Timothy: Paul
- 2 Timothy: Paul
- Titus: Paul
- Philemon: Paul
- Hebrews: Paul
- James: James (Jesus’ brother)
- 1 Peter: Peter
- 2 Peter: Peter
- 1 John: Apostle John
- 2 John: Apostle John
- 3 John: Apostle John
- Jude: Jude (Jesus’ brother)
- Revelation: Apostle John
Notice that Moses was the writer for the book of Job. You can find more information about how we know who the writers were in the book "All Scripture Is Inspired of God and Beneficial". However, note the acknowledgement at the end of the table (from the first link):
Names of writers of some books and of places where written are
uncertain. Many dates are only approximate, the symbol a. meaning
“after,” b. meaning “before,” and c. meaning “circa,” or “about.”