This paper describes a potential-based panel method for the prediction of unsteady performance of a marine propeller operating in a non-uniform flow field. Boundary-value problem, formulated by distributing the normal dipoles and sources on the blade, the hub and the shed wake, is descretized and numerically analyzed in a discretized time domain. Through an extensive test and comparison with the analytic solution, the convergence in time step is verified for a two-dimensional foil. Unsteaty analysis is then carried out for the DTRC 4118 propeller operating in a harmonic wake, and compared favorably with the experimental result. The present method is shown applicable to the analysis of unsteady performance of the propellers.