According to the Gospel of Matthew, Christ was born during the reign of King Herod. Since it is reported in the same Gospel that Herod was succeeded by his son Archelaus, therefore we can be sure that the Evangelist wrote about King Herod the Great. It should be noted, it is not sure when exactly Herod the Great died, depending on the Historians the date varies between 1 BC and 4 BC. So it can only be stated that according to the Gospel of Matthew, Christ was born prior to 1 BC.

Matthew 2
16 Then Herod, when he saw that he was mocked of the wise men, was exceeding wroth, and sent forth, and slew all the children that were in Bethlehem, and in all the coasts thereof, from two years old and under, according to the time which he had diligently inquired of the wise men.
17 Then was fulfilled that which was spoken by Jeremiah the prophet, saying,
18 In Rama was there a voice heard, lamentation, and weeping, and great mourning, Rachel weeping for her children, and would not be comforted, because they are not.

Matthew 2
22 But when he heard that Archelaus did reign in Judaea in the room of his father Herod, he was afraid to go thither: notwithstanding, being warned of God in a dream, he turned aside into the parts of Galilee:

On the other hand according to the Gospel of Luke. During a Census ordered by Caesar Augustus, Joseph traveled to Bethlehem with Mary where Christ was born. Luke also mentioned Cyrenius the governor of Syria. Cyrenius is the name in the Greek Language for Publius Sulpicius Quirinius. Cyrenius was governor of Crete and Cyrene around 14 BC, he became Consul in 12 BC. In 6 AD he became (Governor) Legate of Syria, a high ranking officer of the Roman Army. In 6 AD, Cyrenius conducted the Census of the Roman Province Judea.

As you saw earlier, the Gospel of Matthew places the Birth of Christ prior to 1 BC. On the other end the Gospel of Luke seems to indicate that Christ was born during the Census which appears to have taken place in 6 BC according to Historians. Some folks believe there may have been another Census prior to 6 AD. I highly encourage readers to investigate this matter and establish the Truth.

Luke 2
1 And it came to pass in those days, that there went out a decree from Caesar Augustus that all the world should be taxed.
2 (And this taxing was first made when Cyrenius was governor of Syria.)
3 And all went to be taxed, every one into his own city.
4 And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David:)
5 To be taxed with Mary his espoused wife, being great with child.