We present a framework for a pragmatic science of cultural evolution. It is now possible for behavioral science to systematically influence the further evolution of cultural practices. As this science develops, it may become possible to prevent many of the problems affecting human wellbeing. By cultural practices, we refer to everything that humans do, above and beyond instinctual or unconditioned behaviors: not only art and literature, but also agriculture, manufacturing, recreation, war making, childrearing, science-everything. We can analyze cultural practices usefully in terms of the incidence and prevalence of individual behavior and group and organization actions. An effective science of intentional cultural evolution must guide efforts to influence the incidence and prevalence of individuals' behaviors and the actions of groups and organizations. In this paper, we briefly sketch advances in scientific understanding of the influences on individual behavior. Then we describe principles that could guide efforts to influence groups and organizations. Finally, we discuss legitimate concerns about the use and misuse of a science for intentional cultural change.