Alfred Robert Gaul (30 April 1837 — 13 September 1913) was an English composer, conductor and organist.
Gaul was born in Norwich, where he studied under Zechariah Buck. By the age of nine he was a chorister at Norwich Cathedral, and at the age of seventeen he was appointed as the organist of the parish church at Fakenham. In 1859 he moved to Birmingham, where at the age of twenty two he was appointed organist at St. John's Church, Ladywood. In 1863 he took the Bachelor of Music degree at the University of Cambridge. He was Master of Music at St Augustine's Church, Edgbaston from 1868, the first Birmingham church to have a surpliced choir.
In 1877 Gaul started teaching the first classes in the theory of music, harmony and counterpoint at the Birmingham and Midland Institute, marking the first step towards providing a fully rounded musical instruction at the institution that would eventually become Birmingham Conservatoire. He would later be appointed as professor of orchestration and composition at the school. He taught singing and harmony at the King Edward VI High School for Girls.