The invention discloses a screw type single-machine three-stage compression heat pump heating system and a control method. The system is characterized by comprising a single-machine three-stage screwtype compressor, and a refrigerating fluid inlet, a refrigerant outlet, a first air supplementing port, a second air supplement port and an oil return port are formed in the single-machine three-stagescrew rod type compressor. The refrigerant inlet is connected with a gas-liquid separator, and the refrigerant outlet is connected with an oil separator; the first air supplementing port is connectedwith a second economizer, and the second air supplementing port is connected with a first economizer in a cast-in mode; and an oil outlet of the oil separator is connected with an oil cooler, then the oil outlet of the oil separator is sequentially connected with an oil filter, the electromagnetic valve and an oil flow switch, finally the oil outlet of the oil separator is connected with an oil return port of a single-machine three-stage screw type compressor. The problems that an existing air source heat pump exceeds a limit value due to the compression ratio, the water outlet temperature islow, the application environment range is narrow are solved, the technical scheme can be applied to all heating areas in China, a traditional coal-fired boiler can be directly replaced, the installation and modification are convenient, the economic and rapid effects are achieved, the energy is saved, the environment is protected, and the technical scheme is a good heating technical scheme.