Anderson was born in Kirkman, Iowa, the son of a railroad telegrapher. He began playing his sister's clarinet when she tired of it, and by high school had formed his own dance band. After a year in junior college in Fort Dodge, Iowa, he received a music scholarship to Drake University in Des Moines. He attended for two years, but then quit school to begin his professional musical life by accepting a job with the Lee Barron Orchestra, a territory band based out of Omaha.