This clutch control device is provided with: a supply valve and a supply valve control unit, which control the supply of an operating fluid to a pressure chamber; a first discharge valve and a first discharge valve control unit, which control the discharge of the operating fluid in the pressure chamber; and a second discharge valve and a second discharge valve control unit, which control the discharge of the operating fluid in the pressure chamber. When it is determined that the engagement and disengagement switching of a clutch device 2, which is necessitated by the discharge of the operating fluid in the pressure chamber, is required, the first discharge valve is controlled to be opened and then the second discharge valve is controlled to be opened.