A clutch control device includes a clutch apparatus configured to connect and disconnect power transmission between an engine and a gearbox, a clutch actuator configured to output a driving force to actuate the clutch apparatus, and an ECU configured to drive the clutch actuator, and the ECU performs engine stalling avoiding control which decreases a clutch capacity when a reduction speed of an engine rotational speed becomes a predetermined threshold or more and the engine rotational speed becomes a predetermined engine stalling determination value or less.