Smith was the son of Thomas, the rector of Marston Moretaine, Bedfordshire, who owned land in three counties.
[4] Smith died on 22 June 1667 and was buried in the chancel of Kings Nympton church.
He wrote satirical poetry, which was published in a collection entitled Musarum Deliciæ or the Muses' Recreation, in 1656.
Smith's verses appear to have been written for amusement in correspondence with Sir John Mennes, whose replies were also included.
The publisher, Henry Herringman, stated that the poems had been collected by him from "Sir John Mennis and Dr. Smith's drolish intercourses."