The invention relates to a solid-liquid dual-mode attitude and orbit control power system and a control method thereof in the field of space propulsion systems. The solid-liquid dual-mode attitude and orbit control power system comprises a controller, a fuel gas generator, a gas collection tank, a propellant storage tank, a fuel gas attitude control thruster and a liquid orbit control engine. A solid grain is arranged in the fuel gas generator, the fuel gas generator, the gas collecting tank, the propellant storage tank and the liquid orbit control engine are sequentially communicated through pipelines, the gas collecting tank is communicated with the fuel gas attitude control thruster through a pipeline, and the controller is used for controlling the system. The controller controls the fuel gas generator to ignite the solid grain, the solid grain combusts to generate high-pressure fuel gas, the high-pressure fuel gas is filled into the gas collecting tank, one path of the high-pressure fuel gas in the gas collecting tank enters the fuel gas attitude control thruster, and the other path of the high-pressure fuel gas in the gas collecting tank enters the propellant storage box to extrude a propellant into the liquid orbit control engine. The advantages of a solid gas pressurization system and a liquid propelling system are combined, normal-pressure prepackaging storage of the propelling system is achieved, and the safety of prepackaging storage is improved.