A new cyclic model of a class of chemical pumps affected by the irreversibility of mass transfer is set up. With the help of optimal control theory, the optimal cyclic configuration of the chemical pumps is determined and its fundamental optimal relation is derived. Other optimal performances of the cycle are discussed. The differences between the chemical pump and the chemical engine and between the chemical pump and the conventional heat pump are compared. The results obtained here can provide some new theoretical instructions for the optimal design of a class of apparatus such as mass exchangers, as well as electrochemical, photochemical, and solid-state devices, the fuel pumps for solar-energy conversion systems.