The invention relates to an internal-combustion engine with two-phase inner cam shock wave shifting for transmission, relates to the field of gas power, and belongs to a multi-cylinder internal-combustion engine. The invention provides a novel internal-combustion engine, wherein eight air cylinders are symmetrically uniformly distributed on the periphery of a two-phase inner cam in an annular manner, the stressed resultant force of a convex inner two-phase inner cam is zero, an air cylinder piston is directly acted on the convex inner two-phase inner cam through a push rod, and power is passed on an output shaft connected with a center wheel key through two-phase inner cam shock wave moving teeth of the convex inner two-phase inner cam. In the internal-combustion engine, a connecting rod and a crank shaft of the traditional internal-combustion engine are omitted, and a convex inner two-phase inner cam shock wave shifting transmission mechanism has no eccentric quality, has inertia force and service load self balancing; and the rotation speed of the output shaft depends on the transmission ratio of the living teeth transmission, if a living teeth frame is fixed, a center wheel outputs at a low speed in a large torque, and the internal-combustion engine is broadly used to project machines, armored cars and the like which need high power. The internal-combustion engine provided by the invention has the advantages that the structure is simple and compact, the axial size is small, the stressing is self-balanced, and the operation is stable.