The invention discloses a power system of an all-wheel-drive hybrid power automobile and a control method. The power system comprises an engine, a first motor, a first inverter, a front-axle planet gear reducer, a second motor, a second inverter, a rear-axle reducer and a battery; the power system only comprises two motors and a set of simple planet gear mechanism and is relatively lower in cost, under the pure electric mode, the free selection of front-drive, rear-drive and all-wheel-drive can be achieved, the first motor further has two selectable gears, the opportunity of working at optimum efficiency is improved, and the pure electric economy is improved. Under the engine mode, starting and low-speed driving of the automobile can be achieved through the electronic stepless variable speed function, and the economy of low-speed driving of the automobile is improved. The engine has three selectable fixed gears which are used for direct driving in medium-high speed cruising, high-efficiency characteristics of the engine in high-load are used, the damage of electrical paths due to the electronic stepless variable speed is avoided, and the transmission efficiency is improved.