A simple surface panel method has been successfully applied to steady or unsteady wing problems. This method uses source distributions (Hess and Smith type) on the wing surface and vortex distributions arranged on the camber surface according to Lan's quasi-continuous vortex lattice method (QCM). We named this method SQCM (Source and QCM). In this paper, we apply SQCM to the unsteady propeller problem by combining the source panels and unsteady QCM which has been successfully developed. We consider the unsteady Kutta condition that the pressures must coincide with each other on the upper and lower surfaces at the trailing edge. In the steady problem, SQCM satisfies the Kutta condition by setting zero normal velocity at the trailing edge on the camber surface. But it is not usually equal to zero in the unsteady problem but a finite normal velocity exists. In the unsteady two or three-dimensional wing problem, we obtained this normal velocity by iteration for the equal pressure condition at the trailing edge. We show numerical results for two kinds of full-scale propellers (Seiun-maru's conventional and highly skewed propellers) in non-uniform flow. Pressure distributions obtained by the present method are in good agreement with experimental data and thrust fluctuations of one blade and the propeller are plausible.