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Peristaltic pumping by wavelike contractions is a fundamental biomechanical mechanism for fluid and material transport and is used in the esophagus, intestine, oviduct, and ureter. While peristaltic pumping of a Newtonian fluid is well understood, in many important settings, as in the fluid dynamics of reproduction, the fluids have non-Newtonian responses. Here, we present a numerical method for simulating an Oldroyd-B fluid coupled to contractile, moving walls. A marker and cell grid-based projection method is used for the fluid equations and an immersed boundary method is used for coupling to a Lagrangian representation of the deforming walls. We examine numerically the peristaltic transport of a highly viscous Oldroyd-B fluid over a range of Weissenberg numbers and peristalsis wavelengths and amplitudes.