A clutch control apparatus mounted at a vehicle where a clutch (2) is arranged at a power transmission passage between a transmission (3) and an internal combustion engine (1), the clutch control apparatus includes a controlling portion (30) controlling the internal combustion engine (1) which is in a stopped state to automatically start, controlling a clutch actuator (21) in response to a depression of the acceleration pedal (15) at a time the clutch pedal (13) is shifting to the engagement state after the internal combustion engine (1) is automatically started, and controlling the clutch actuator (21) to achieve a creep start of the vehicle in a case where the acceleration pedal (15) is not depressed at a time the clutch pedal (13) is shifting to the engagement state after the internal combustion engine is automatically started.