In this paper, Brownian configuration fields (BCF) with the finite volume discretization on non-staggered grids is employed to simulate 2D viscoelastic fluid flows. In order to verify the effectiveness of the numerical method, the plane Couette flow is firstly tested, and the resu-lts are compared with the available literature data. Then, the BCF method is extended to the planar contraction flow. The influence of We on the flow patterns is also analyzed. All numerical results illustrate that the numerical method employed in this paper has the advantages of high efficiency and good stability, and is easy to deal with the convection term. Furthermore, it is observed that the variance reduction can nicely suppress the unphysical oscillation of stress around the contraction corner.