A twin clutch speed-change apparatus that can reduce shift shock includes a transmission with multiple gear pairs disposed between a main shaft and a countershaft. A twin clutch is provided on the main shaft, a rotational drive force from an engine being connected/disconnected between the transmission and the engine, a dog clutch is provided between an axially slidably attached slidable gear and an axially non-slidably attached non-slidable gear to select a gear pair, for transmitting a rotational drive force, from the multiple gear pairs. Dog teeth of the dog clutch include steps different in axial height from each other between a portion abutted against a lateral wall surface of a dog hole when the rotational drive force is transmitted by the dog clutch, and a portion abutted against a lateral wall surface of the dog hole when the rotational drive force is not transmitted by the dog clutch.