Hancock was born in Springfield, Massachusetts. In 1830, while living in Ohio, Hancock heard Latter Day Saint missionaries Parley P. Pratt, Sidney Rigdon, and Oliver Cowdery preaching in Mayfield. Convinced by their words, Hancock was baptized in the Latter Day Saint church. Hancock was ordained an elder shortly after his baptism and in 1831 he served a mission to Missouri with Zebedee Coltrin.
In 1834, Hancock participated in Zion's Camp, traveling from Ohio to Missouri in an effort to assist Latter Day Saints experiencing trouble. On March 1, 1835, Hancock was ordained a seventy in the church and was selected as one of the first seven presidents of the Seventy. On April 6, 1837, Hancock was released from this position because it was mistakenly believed that he, like five of the other presidents of the Seventy, had already been ordained a high priest. When it was discovered that this was not the case, Hancock was restored to his position on September 3, 1837. Hancock would serve as one of the presidents of the Seventy until his death.
Hancock wrote the words to several songs. His "My Peaceful Home, 1837" captures the feelings of Latter-day Saints about their new homes in the communities they had set up. Hancock wrote the words of the twelve verse song sung at the placing of the Far West Temple cornerstones in 1838.
Hancock followed the Latter Day Saints as they moved to Missouri, and then to Nauvoo, Illinois. He was a member of the Nauvoo Legion and the Nauvoo police force. In 1843 Hancock was made the chief musician in the Nauvoo Legion.
In 1844, Hancock became a member of the Council of Fifty, and in 1846 joined the Mormon Battalion. In 1847, Hancock traveled with the Mormon pioneers to the Salt Lake Valley. In Utah Territory, he became a member of the 1st Utah Territorial Legislature. He served a full time mission for the church attempting to grow cotton in southern Utah. Hancock helped settle Washington, Utah, and was ordained a church patriarch in 1872. He died at Washington, Utah.
Like many early Latter Day Saints, Hancock practiced plural marriage. Hancock was married to five wives, three of whom eventually divorced him; he was the father of 18 children.