A proper vertex coloring of a graph is acyclic if contains no bicolored cycle. Given a list assignment of , we say is acyclically -list colorable if there exists a proper acyclic coloring of such that for all . If is acyclically -list colorable for any list assignment with for all , then is acyclically -choosable. In this paper we prove that planar graphs without 4, 7, and 8-cycles are acyclically 4-choosable.