A heat pump with low power consumption and a simple mechanical configuration is required to save energy and reduce carbon dioxide emissions. We show the design and demonstration of a novel heat pump using a Knudsen compressor, referring this device as a Knudsen heat pump. Water is employed as a refrigerant. The motionless nature of the Knudsen heat pump is accomplished by using a Knudsen compressor to transport the refrigerant vapor from the evaporator to the condenser, and thermal energy alone supplies the needed power. We employ a simple single-stage Knudsen compressor powered by light from a halogen lamp as an energy source. Experiments confirmed heat transport from the evaporator to the condenser with an output power of 3.09 W. The output power tended to increase linearly as the temperature difference between the evaporator and condenser decreased. The pressure-enthalpy diagram of the proposed Knudsen heat pump cycle was shown, and the thermal efficiency of this heat pump was analyzed. The application of a multi-stage Knudsen compressor to improve the heat pump performance was also discussed. This heat pump is free from noise, vibration, and maintenance, and it can utilize low-quality energy, such as a solar energy, and it does not require any electrical input. These properties make the Knudsen heat pump a particularly significant technology in harsh environments such as space and desert.