The large eddy simulation methodology is applied to predict the flow around a marine propeller in the forward and crashback modes of operation. A non-dissipative, robust numerical algorithm developed by Mahesh et al. (2004, J. Comput. Phys., 197: 215-240) for unstructured grids was extended to include the effect of rotating frame of reference. The thrust and torque coefficients, circumferentially averaged mean velocity and root mean square fluctuation of velocity obtained from the simulation are compared to experimental data and good agreement is observed. The crashback simulations show the presence of a highly unsteady ring-vortex, and irregular low frequency unsteady loads on the propeller.