The Church of Jesus Christ of Latter-day Saints has not officially declared this as church doctrine2 but this knowledge is generally accepted throughout the church and has been support by our prophets, apostles, and other general church leaders.
Elder James E. Talmage, a member of the Twelve Apostles (from 1911-1933) and noted Mormon scholar, said, "We believe that Jesus Christ was born in Bethlehem of Judea, April 6, B.C. 1."3
President Gordon B. Hinckley, 15th president of the Church, said:
"Men had no knowledge of the time of His birth, and so they came to bond the celebration of Christmas with the celebration of the return of the sun. While we now know through revelation the time of the Savior's birth [April 6], we observe the 25th of December with the rest of the Christian world.4"Although we celebrate Christmas and the birth of Jesus in December, we should remember our Savior and His atonement throughout the entire year. Continue learning about the Birth and Life of Jesus Christ.
1 See D&C 20:1.
2 John P. Pratt, "The Restoration of Priesthood Keys on Easter 1836, Part 1: Dating the First Easter," Ensign, Jun 1985, 59.
3 Jesus the Christ: A Study of the Messiah and His Mission According to the Holy Scriptures Both Ancient and Modern, 32d ed. Salt Lake City: The Church of Jesus Christ of Latter-day Saints, 1946, p. 104.
4 "Christmas Devotional with First Presidency," Ensign, Feb. 1998, 74–75.