Absolutely Yes! Allow me to explain.
First, it follows logically that if the Bible is the word of God (which it claims to be over 3,000 times in various ways), and God cannot lie (Heb. 6:18), then the Bible cannot be in error.
Second, Jesus taught that the Old Testament was inerrant. He said , “I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished” (Matt. 5:18). He also said that the Scripture cannot be broken (John 10:35). He may have also taught that the New Testament was inerrant in John 16:13. Jesus told His disciples that after He departed, the Holy Spirit would guide the disciples “into all truth.”
The New Testament authors certainly believed the Old Testament was inerrant. Paul told Timothy that “All Scripture is God-breathed and is useful teaching, rebuking, correcting and training in righteousness…” (2 Tim. 3:16). This was written near the very end of Paul’s life (since he mentioned his impending death in the next chapter). It is very interesting that in his earlier letter to Timothy, Paul called the Gospel of Luke Scripture and placed it on the same level as the Old Testament (1 Tim. 5:18). Peter called Paul’s writings Scripture in 2 Peter 3:15-16.
Third, there has never been one fact of history, science, archaeology, etc., that contradicts the Bible. Many have claimed that science contradicts the Bible, but the Bible actually provides the only basis for science. This topic is covered in greater detail in my first book, Old-Earth Creationism on Trial.
In Volume I of his Systematic Theology (p. 495), Norman Geisler summarizes five reasons to believe in biblical inerrancy based on statements from Scripture:
1) That it is God-breathed.
2) That it is a prophetic writing.
3) That it has divine authority.
4) That it is what God says.
5) That it is called “the Word of God” or the like.
Finally, it is important to understand what the doctrine of inerrancy actually states. It is that the entire Bible is without error in the original manuscripts. The last two words are key, because there are some versions/translations today that have some minor copyist errors (by minor, I mean that a number or word is transposed or some other common typographical error.) This takes us into the realm of textual criticism, which is an entirely different subject.
For more on that particular issue, check out an article I wrote for the Answers in Genesis website on whether the Bible is authoritative and inerrant. I would also recommend Dr. Gleason Archer’s detailed discussion of textual criticism in A Survey of Old Testament Introduction.