The performance of an irreversible engine consisting of a nonlinear diodes system is presented. The system consists of two diodes switched in the opposite directions and located in two reservoirs at different temperatures, and the two diodes are connected in parallel with a capacitor. Based on the theory of thermal fluctuations, the expressions of the heat fluxes absorbed from the hot and cold reservoirs are derived. When the heat leak between the two reservoirs is taken into account, the power output and the efficiency of the engine can be obtained. The performance characteristic curves are plotted and the characteristic relations between the optimum performance parameters and the ratio of the temperatures are obtained by numerical simulation. The influence of the main parameters, including the nonlinearity of the diodes, the loss of heat leak and the ratio of temperatures of two reservoirs, on the performance characteristics of the engine is analyzed in detail. Finally, the performance characteristics of the ideal diodes engine are discussed.