This paper presents the possibility of reducing the demand for nonrenewable primary energy for buildings using a new conceptual adsorption system of cooling and heating supplied by solar energy. Moreover, the aim of this study is to shorten the payback time of investment in the standard adsorption cooling system through its integration with the heating system. Research has been carried out for an energy-efficient medium-sized single-family building with a floor area of 140 m2 and a heat load of 4.2 kW and cold load of 4.41 kW. It has been shown that the use of an adsorption system of cooling and heating supplied by solar energy decreased the demand for nonrenewable primary energy by about 66% compared to the standard building that meets the current requirements.