This paper concerns the prediction of the power outputs of wave energy converters (WECs) operating in shallow water nonlinear waves. The bottom effects on the power performances of WECs (a phenomenon that has always been overlooked by the previous researchers) have been taken into account during the calculations. Using an oscillating surge wave energy converter (OSWEC) as an example, it is demonstrated in this article that for each sea state using linearly simulated waves without bottom effects as inputs in the simulation will always predict the OSWEC's power output more than 200% higher than the result predicted by inputting nonlinearly simulated waves with bottom effects. Therefore, nonlinear simulated waves with bottom effects should instead be utilized as inputs in the simulation process. In order to further improve the simulation efficiency, a novel transformed linear simulation method is first proposed in this paper for generating equivalent waves as those obtained from the nonlinear simulation method. Further calculation examples show that the relative error of the predicted power output value when inputting transformed linearly simulated waves is always less than or equal to 1.97%.