The invention provides a power system of a dimethyl ether/hydrogen internal combustion engine and a control method for the power system of the dimethyl ether/hydrogen internal combustion engine, belonging to the fields of energy saving and the use of alternative fuels of the internal combustion engine. The power system comprises a dimethyl ether gas supply device and a hydrogen gas supply device, wherein dimethyl ether is reformed to produce hydrogen by the waste heat of the tail gas. The power system also comprises a dimethyl ether tank and a hydrogen tank, a tail gas waste heat reforming device, a blended fuel control unit and a dimethyl ether reformer controller, and input signals such as a crank angle signal, a cooling water temperature signal, a gas inlet temperature and pressure signal, and output signals such as a dimethyl ether jetting signal and a hydrogen jetting signal, an igniting module signal, an idle speed motor control signal, and a tail gas waste heat reforming device control signal. According to the invention, the discharging performance and the combustion performance of a spark ignition engine can be improved and increased due to dimethyl ether and hydrogen, and hydrogen is produced by reforming dimethyl ether, so that the use cost can be reduced, and the compensation of hydrogen can be realized. The device is simple in design structure, easy to install, and lower in cost, and the system is further good in adaptability and expansibility, wide in market prospect, and better in economic benefit.