The goving equation about steady flow of viscoelastic fluids in an eccentric annulus with inner rod moving axially is established by using common conversion Maxwell constitutive model. The numerical solutions of the flow are obtained by control volume and ADI methods. The influence of the eccentricity, velocity of inner rod and elasticity of fluid to the velocity distribution, flow rate and radial force on the inner rod is obtained, and the reason for the severe eccentric wear of the sucker rod of polymer-flood well is analyzed.