A solar-driven Stirling heat engine system composed of a Stirling heat engine, a solar collector, and a heat sink is presented, in which the radiation and convection heat losses of the solar collector, the heat-leak between the thermal absorber and heat sink, the regenerative losses of the Stirling heat engine, and the energy balance between the thermal absorber and the high isothermal process of the Stirling heat engine are taken into consideration. Based on the irreversible thermodynamics and Lagrange multiplier method, the maximum power output and the corresponding optimal efficiency of the system are determined and the absorber temperature that maximizes the optimal system efficiency is calculated numerically. The influences of some system parameters such as the concentrating ratio, the volume ratio during the regenerative processes and irreversibilities of heat exchange processes on the optimal efficiency are analyzed in details. The results obtained here may provide a new idea to design practical solar-driven Stirling heat engine system. (C) 2015 Elsevier Ltd. All rights reserved.