In 1932, a group of Catholics bought a five-acre tract of land at the corner of Laurel and Cedar Streets from the Ursuline Sisters in Galveston. Later, they built a building for classrooms and gatherings. Bishop Christopher E. Byrne granted permission for this building to be converted into a chapel, and Father Thomas Carney, Pastor of Dickinson, offered the first Mass on October 26, 1941. Father Frank A Lagana was an Assistant pastor to Father Carney at this time, and Queen of Peace was a mission of Dickinson for the next ten years.
 
On August 10, 1951, the mission Queen of Peace, La Marque, was granted PARISH status, and Father Frank A. Lagana was named the first pastor. In 1955, the school and convent were constructed in time for the 1955-1956 school year. Kindergarten through the fourth grade was started, and then a grade a year was added until we had through sixth grade in our school. In May 1957, the rectory was completed, and Father Lagana started getting assistant Pastors to help in the parish.
 
In February 1963, the ground was broken for the present Church. The  First Mass was offered in it on December 15, 1963. The solemn dedication of the Church was by Bishop John L. Morkovsky on January 12, 1964.   In the spring of 1983, Monsignor Lagana Pastor and Father Douglas Guthrie were appointed Administrators and later Pastors of the Parish. In March 1986, Monsignor T. Culver was appointed Administrator and later as Pastor of the Parish. Monsignor Culver came here as the Episcopal Vicar for the Southern Vicariate of the Diocese of Galveston-Houston.
 
The Parish Life Center was built under Msgr. Culver’s direction. It has become a gathering place for the parish’s many organizations, celebrations, and events.

Rev. Msgr. Frank Lagana
 1951-1983

 Rev. Fr. Douglas Guthrie
 1983-1986

 Rev. Msgr. Joseph T. Culver
 1986-2008

 Rev. Fr. Chacko Puthumayil
 2008-2021

 Rev. Msgr. James B. Anderson
 2021-