In this article, the Modified Upper-Convected Maxwell equation (MUCM) is proposed. The viscoelastic polymer solution flow characteristics are described by the numerical method. The stream function contour, velocity contour and stress modulus contour of fluid in slot channel are drawn. The non-Newtonian power law property and viscoelasticity of MUCM fluid influence on the stream function are analyzed. The velocity contour move towards dead oil area with the viscoelasticity increase, flow area increase and the sweep area enlarges, so the sweep efficiency is enhanced.