When was the Gospel of Luke written?

Luke wrote his Gospel prior to 62AD. Luke wrote his gospel before he wrote Acts. Acts is known to be written prior to 64AD.

Some people place the time of writing around A.D 56-58 before the death of Paul. Some say after Paul's death but before the sacking of Jerusalem around A.D.60-65
The most likely date for Luke is very early in the 60's of the first century.

Since nearly all agree that Luke must precede Acts in time, and Acts ends about a.d. 63 with Paul in Rome, a date before that is probable. The great fire of Rome and the persecution of Christians as Nero's scapegoats in a.d. 64 would surely have been mentioned by Luke if he was writing after these events.

We can establish an approximate minimum date for when Luke's Gospel was written, by identifying the sources, since the book must have been written after the books Luke used as sources. The author makes it very clear, even in the first verse of Luke that he was not writing a first-hand account, nor one based on witnesses or friends, when he talks of what things "are most surely believed among us".

We know that both Matthew and Luke relied on Mark's Gospel for most of their information about the life of Jesus. Whenever they agree with Mark, the text is almost identical in Greek, somthing that could not happen unless one Gospel was being copied. We also have the "missing block", a short section of text that was obviously missing from the copy of Mark that Luke was using. Since we can say that Mark's Gospel was written approximately 70 CE, Luke's Gospel must have been written some time later. Internal clues indicate that Luke's Gospel must have been written somewhat later than Matthew's, so we can say that Matthew's Gospel would have been written no ealier than 80 CE, while Luke's Gospel was written no earlier than about 90 CE.

Luke's Gospel show evidence of borrowing material from the works of Josephus, a Jewish military leader and historian. Evidence that it contains material from Antiquities of the Jews, written in 93 CE, indicates that it was written some time after this date.

We know that Luke's Gospel was already regarded as a classic of Christian scriptures by the middle of the second century, so we also know that it could not have been written later than the early years of the century.

On the basis of this evidence, we can suggest that the Gospel According to St Luke was probably written in the late 90s of the first century, or quite early in the second century.