To evaluate the actual computational efficiency of the Fourier Time Spectral Method in the aspect of the time-discretization accuracy, accuracy analysis is performed on the computational solutions of two-dimensional transonic flows. Computational results of periodic flows over a pitching NACA0012 airfoil by solving unsteady Euler equations show that large time interval could be used for the Fourier TSM to model periodic transonic flows even when shock waves occur. Error analysis shows that, compared to the 2nd order Backward Difference Formula (BDF) method, the Fourier TSM is much more efficient in predicting the temporal variation of quantities that are integrated from the surface pressure coefficient, especially the lift coefficient. When predicting the temporal variation of the surface pressure coefficient, the computational efficiency of the Fourier TSM is not lower than that of the 2nd order BDF method.