We study the maximum efficiency of a Carnot engine based on a small system. It is revealed that due to the finiteness of the working substance, irreversibility may arise when contacting with a heat bath. As a result, there is a correction to the usual Carnot efficiency. This result defies the usual belief that the Carnot efficiency does not depend on the details of the working substance. Furthermore, we find a general and simple expression for the maximum efficiency of heat engines. This maximum efficiency approaches the usual Carnot efficiency when the dimension of the working substance increases to macroscopic size. Our study demonstrates the subtletis of thermodynamics of small systems.