Muslims can read the Bible, and some do for study, interfaith dialogue, history, or comparison. Islam also teaches that God gave earlier revelation to prophets associated with the Torah, Psalms, and Gospel. However, the Qur’an is the final and controlling scriptural authority for Muslims.

Earlier revelation in Islam
The Qur’an refers to the Torah given to Moses, the Psalms associated with David, and the Gospel given to Jesus. Muslims therefore do not regard biblical figures as foreign to Islam.
Abraham, Moses, David, Mary, and Jesus all have important places in the Qur’an, though their stories can differ from biblical versions.
Is today’s Bible identical to those revelations?
Muslim scholars have developed different explanations of how present biblical texts relate to the original revelations. Some emphasize textual alteration; others focus more on interpretation, selection, or theological misunderstanding.
For that reason, Muslims generally do not treat the present Bible as equal in authority to the Qur’an.
Why Muslims may read the Bible
Muslim students of comparative religion may study the Bible to understand Christianity and Judaism. Scholars of history and language also use biblical texts as part of the wider religious environment of Late Antiquity.
Reading the Bible does not mean accepting Christian doctrines such as the Trinity or the divinity of Jesus.
The Qur’an as final criterion
Mainstream Islam understands the Qur’an as God’s final revelation to Muhammad and as reliably preserved for the Muslim community.
When biblical and Qur’anic accounts differ, Muslims normally give religious priority to the Qur’an.
Short answer
Muslims may read the Bible, but Islamic belief gives final scriptural authority to the Qur’an and interprets earlier revelation through an Islamic framework.