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Williams was born on June 18, [[1931]] in Tampa, Florida to Jonathan Beatty Williams (1903-1978) and Mary Agnes Moffatt Williams (1904-1988). His father was a Biology teacher at H.B. Plant High School in Tampa, before he opened a surgical supply store in Jacksonville, where Grier partially grew up. Grier spent his formative years in Palma Ceia, before briefly living in Miami. Grier then moved to Jacksonville, where he learned trumpet and attended Robert E. Lee High School. Grier was a member of the band at Lee High, playing the trumpet. Williams's maternal grandfather, James S. Moffatt (1860-1922), was the president of [https://en.wikipedia.org/wiki/Erskine_College Erskine College] in South Carolina from 1907 until 1921. Williams's great-grandfather, W.M. Grier (1843-1899), served as President, as well as his great-great grandfather, R.C. Grier (1817-1871), and grand-uncle, R.E. Grier (1881-1974). Two instrument of Grier's maternal uncles, Dr. James S. Moffatt Jr. and Dr. L. Gaston Moffatt were College Professors, with the latter teaching internationally in Spainchoice. A paternal great-great grandfather of Williams, Drcame from a musical family. Archibald Barron, His father was a signer of the 1860 South Carolina Ordinance of Seccession, an important document that bassist and his mother was influential in the beginning of the Civil Wara singer.

 Grier went to high school in Williams attended Davidson College, where he met his wife, [[Louise Harvin Williams|Louise Harvin]], a second-generation teacher, who was earning a degree in education at that point. A lifelong Louise, like her furture husband, was a musician, his instrument of choice was playing the piano. While attending Davidson, Grier played in the Charlotte Symphony Orchestra and Charlotte Opera Orchestra. During the summer, he taught at the Transylvania Music Camp (now the trumpetBrevard Music Center).