The optimal configuration of an endoreversible heat-engine with the linear phenomenological heat-transfer law q proportional to Delta(T-1), has been determined. The optimal cycle that maximizes the power-output of the heat-engine has been obtained using optimal control theory. It is shown that the optimal cycle has six branches including two isothermal ones, four maximum power branches, and is without an adiabatic branch. The interval of each branch, the temperatures of the heat reservoirs and working fluid, the maximum power and the corresponding efficiency of the heat-engine are obtained. The results are compared with those obtained assuming Newton's heat-transfer law applies. (c) 2007 Elsevier Ltd. All rights reserved.