He was a native of Lancashire, elected king's scholar of Brasenose College, Oxford, in 1574, and matriculated there on 20 December 1577.
He took holy orders when B.A., and, according to Anthony Wood, ‘became a goodly divine’ and a noted preacher.
At the suggestion of friends, Parkes wrote anonymously his Brief Answer to certain Objections against Christ's Descension into Hell, sent in writing by a Minister unto a Gentleman in the Country.
This was answered by Willet in his Limbomastix, also published anonymously, in which his unknown opponent is styled a ‘Limbist,’ and is accused of sympathy with Cardinal Bellarmine.
In 1607 Parkes published under his own name An Apology of three Testimonies of Holy Scripture concerning the Article of our Creed, He descended into Hell.