The equation governing the unsteady flow of viscoelastic fluids in an eccentric annulus was derived by using the common conversion Maxwell fluid constitutive equation and then discretized by the control volume method. The velocity distribution of flow field was computed by using the ADI method. The influences of the pressure gradient, eccentricity, stroke length, and stroke frequency on the velocity and flow capacity in the flow field was analyzed. The foundation for further research of the eccentric wear problem of the pumping rod in polymer-flood well was laid.