A Riemannian manifold is said to be recurrent if the Riemannian curvature tensor R is recurrent. On the other hand, A. Oubina defined a new class of almost contact metric manifolds, named trans-Sasakian manifolds, which is a generalzation of Sasakian and Kenmotsu manifolds. In this paper, first we define the notion of a recurrent trans-Sasakian manifold. Then we give an information on the recurrent form on a recurrent trans-Sasakian manifold. Using this result, we show that the Riemannian curvature tensor, the Ricci tensor and the scalar curvature on a recurrent trans-Sasakian manifold are expressed in terms of the associated functions. Finally, we show that the recurrent form of a recurrent trans-Sasakian manifold is written by the associated functions.