A construction for retractable state-nite automata without outputs has been given by Nagy. Retractable automata are automata all whose sub automata are retracts of it, and retracts are the subobjects whose related inclusion morphism have a left inverse. Studying retracts is an important subject in dierent branches of mathematics as well as computer science. In this paper, following Nagy's works, we study retractable nitely supported Cb-sets. The category of nitely supported Cb-sets introduced by Pitts is equivalent to one of the presheaf categories of Bazem, Coquand, and Huber. We characterize retractable nitely supported Cbsets as ones which have a decomposition into retractable components. We also give a description of retractable cyclic nitely supported Cb-sets. Furthermore, recalling the notion of s-separated nitely supported Cb-sets, and support maps, we construct a subcategory of nitely supported Cb-sets consisted of s-separated nitely supported Cb-sets with 2-equivariant support maps, and characterize its retractable objects.