The invention relates to a rotary-cylinder engine. The rotary-cylinder engine comprises a shell, a rotary cylinder, an output shaft and a piston assembly. The shell comprises a first cylinder body and a second cylinder body, and an air inlet, an ignition opening and an air exhaust opening are formed in the side wall of the first cylinder body along the circumference. The rotary cylinder is rotatably arranged in the first cylinder body, the ignition opening and the air inlet are arranged in a staggered manner in the rotation direction of the rotary cylinder, and the air exhaust opening and the ignition opening are arranged in a staggered manner in the rotation direction of the rotary cylinder. The output shaft is rotatably arranged in the second cylinder body, and the rotation axis of the rotary cylinder is perpendicular to that of the output shaft. The piston assembly comprises a piston body and a connecting rod, the piston body is movably arranged between the first position and the second position in the axial direction in the rotary cylinder and rotationally matched with the inner wall face of the rotary cylinder, the other end of the connecting rod is rotationally connected with the output shaft, and the output shaft is driven to circularly rotate when the piston assembly axially moves. The engine with the rotary cylinder is simple in structure and low in cost, and four-stroke working of the engine can be met by only drilling a hole in the rotary cylinder.