This paper has studied the thermodynamic performance of a Brownian heat engine, which is driven by temperature difference. Brownian particles move in the periodic double-barrier sawtooth potential with an external load force and contact with an alternating hot and cold reservoir. The kinetic energy change of the Brownian particles and the heat leak between hot and cold reservoir are considered simultaneously. The influence of the main parameters, including the height of barrier, the ratio of the low barrier to high barrier and the external load force, on the efficiency of Brownian heat engine is discussed in detail. When the heat leak between the two reservoirs is taken into account, the Brownian heat engine is irreversible, the efficiency is less than the Carnot efficiency. When the heat leak is small, the ratio of the low barrier to high barrier can increase the efficiency. The curve of the power output versus the efficiency is a loop-shaped one. When the heat leak is negligible, the curve of the power output versus the efficiency is an open-shaped one. The efficiency is still less than the Carnot efficiency, because the heat flow via kinetic energy change of the particles is irreversible.