A computational model is proposed for simulating the flow of polymer nanocomposites. This model is based on a multiphase suspension of disc-like particles and polymers. The particles are represented by oblate spheroid particles that interact with each other via the Gay-Berne (GB) potential, and the polymers are modeled by finitely extensible nonlinear elastic (FENE) chains that interact with each other via the repulsive Lennard-Jones potential. The interaction between an oblate spheroid particle and a FENE chain is also considered using a modified GB potential. A Brownian dynamics simulation of the shear flows of this system was conducted to investigate the orientation behavior of disc-like particles and the rheological properties of this system. The orientation of disc-like particles was affected by polymers, and the particles in a suspension were well aligned in flows because of the flow orientation property of polymers. The predicted shear viscosity exhibited shear thinning, and the normal stress differences agree qualitatively with experimental measurements of polymer/clay nanocomposites. The simulation results suggest that the present model has the potential to be used as a computational model for polymer nanocomposites.