The discrete for the convection term is one of the main difficulties for the num-erical solution of viscoelastic fluid flow. In this paper, for the conservation equations and the Oldroyd-B constitutive equation, a deferred correction method coupled with high order Q-QUICK scheme for the computation of the convection flux is proposed. This method is designed based on the finite volume method on unstructured collocated grids. The planar poiseuille viscoelastic flow is simulated numerically to verify the high precision and stability of the proposed method. In the simulation of 4:1 contraction viscoelastic flow, the changes of the stream lines and stresses as well as growing of the salient corner vortex versus the Weissenberg numbers are revealed. The numerical results show that the numerical method is capable of expanding the range of the Weissenberg numbers for nonlinear viscoelastic fluid.