A new cyclic model for the behaviour of a four-reservoir endoreversible chemical pump is proposed. The optimal relation between the coefficient of performance and the rate of energy pumping is derived by using finite-time thermodynamics or thermodynamic optimization. The optimal times of the four mass-transfer processes are also obtained. Moreover, the effects of the cyclic parameters on the coefficient of performance and the rate of energy pumping are studied by detailed numerical examples. (c) 2006 Elsevier Ltd. All rights reserved.