A novel integrated scheme for modeling incompressible polymer viscoelastic fluid flows is proposed. Lattice Boltzmann method (LBM) is incorporated into finite volume method (FVM) to solve the incompressible Navier-Stokes equations and the constitutive equation respectively, and is implemented using open source CFD toolkits to predict nonlinear dynamics of polymer viscoelastic fluid flows. The hybrid numerical scheme inherits the efficiency and scalability of LBM and maintains the accuracy and generality of FVM. It has been critically validated using the Oldroyd-B model and linear PTT model under Poiseuille flow, Taylor-Green vortex flow and 4: 1 abrupt planar contraction flow, respectively. The results from the integrated scheme have good agreement with the analytical solutions and the numerical results of other FVM schemes in previous publications. (C) 2014 Elsevier B.V. All rights reserved.