The invention relates to a convex inner two-phase cam rolling shifting transmission internal-combustion engine, relates to the field of fuel gas power, and belongs to a multi-cylinder internal-combustion engine. The invention provides a novel internal-combustion engine, the novel internal-combustion engine is characterized in that eight air cylinders are symmetrically distributed on the periphery of a convex inner two-phase cam in an annular manner, the resultant force of the 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 in a key manner through the convex inner two-phase inner cam and the transmission of two-phase inner cam rolling shifting live teeth. The internal-combustion engine omits a connecting rod and a crank shaft in the traditional internal-combustion engine, and the internal-combustion engine has the characteristics that a convex inner two-phase inner cam rolling shifting transmission mechanism has no eccentric quality, has inertia force and operating load self balancing. The rotation speed of the output shaft depends on the transmission ratio of live teeth transmission, if a live teeth frame is fixed, the low speed high pulling torque of the center wheel outputs, and the convex inner two-phase cam rolling shifting transmission internal-combustion engine is widely applied on fields which need large power such as a project machine, military, excavators and armored cars. 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 in self balancing, and the operation is smooth.