Computational methods based on Cartesian mesh are popular in simulating fluid flow with moving boundaries of complex geometry. In this paper, a sharp-interface Cartesian grid method is proposed for simulating viscoelastic fluid flow. We implement a finite volume numerical scheme with an improved Rhie-Chow interpolation on the open-source toolbox OpenFOAM. In the benchmark test of flow past a stationary cylinder, the velocity for Newtonian fluid flow is found to be second-order accurate with linear/bi-linear fitting functions for local reconstruction and third-order accurate with quadratic fitting functions. Only first-order accuracy is achieved with current solver for the Oldroyd-B fluid flows due to the difficulty in handling the extra stress near the boundary. However, our sharp-interface Cartesian grid method has been verified to correctly predict the extra stress on the surface of the cylinder. Simulation results of confined Oldroyd-B fluid flow past a pair of cylinders are also reported. A comparison between the proposed sharp-interface Cartesian grid method and a smoothed-interface immersed boundary method is carried out with respect to accuracy and efficiency. (C) 2016 Elsevier B.V. All rights reserved.