With the emphasis on energy and environmental protection, energy-conservation and emission-reduction become vital issues for industrial development. Moreover, with the development of legislation on marine environment, the marine diesel engine has become focusing on energy saving and emission reduction for ships. For low-speed diesel engines under high load, waste heat from exhaust gas can be recovered by the compact and efficient gas turbine. In this paper, the matching design research between low speed diesel engine and gas turbine is carried out. To balance efficiency and compactness, the impeller was adjusted and generated by ANSYS BLADEGEN, based on 1D thermodynamic design. And the 1D calculation is similar to the ANSYS CFX simulation result: the total-static efficiency is 73.8% compared to 76.7%. Moreover, the flow separation happened at the impeller suction side and created vortex due to the high incidence angle. The off-design operating point simulation of the turbine shows though the pressure ratio increase will cause the efficiency to decline a little, the total shaft power rises. In sum, this paper worked out a power turbine suitable for a low-speed diesel engine according to the turbine character matching design and simulation, which provides foundation to the construction of a steady operation of waste heat recovery system for marine diesel engine.