An irreversible solar-driven Braysson heat engine system is put forward, in which finite rate heat transfer with the radiation-convection mode from the solar collector to the heat engine and the convection mode from the heat engine to the heat sink, the radiation-convection heat loss from the solar collector to the ambience, the internal irreversibility due to nonisentropic processes in the expander and compressor devices are taken into account. On the basis of thermodynamic analysis method, the analytic expression between the overall efficiency of the solar-driven Braysson heat engine system and the operating temperature of the solar collector is derived and the influences of different heat transfer mechanism, the internal irreversibility parameter, the isobaric temperature ratio, the ratio of heat-transfer coefficients on the optimal performance of the solar-driven Braysson heat engine system are evaluated and depicted quantificationally. The results obtained in the present paper are helpful to deeply reveal the effect of heat transfer mechanism and multi-irreversibilities on the performance of solar driven heat engines.