When engagement of a dog clutch is requested, the dog clutch is engaged while meeting sound vibration performance regardless of whether the main drive wheels are in a non-sleep state. The system for transmitting drive force to the left and right rear wheels (19, 20) comprises a dog clutch (8) and an electronically controlled coupling (16), and a 4WD control unit (34) controls engagement and disengagement of the dog clutch (8) and engagement and disengagement of the electronically controlled coupling (16). In this clutch control device for a 4-wheel drive vehicle, when there is a request to engage the dog clutch (8), which is in a disengaged state, the 4WD control unit (34) first controls engagement of the electronically controlled coupling (16); while doing so, the 4WD control unit (34) monitors the change gradient [Delta]N/dt of the clutch rotational speed difference [Delta]N of the dog clutch (8), and starts engagement of the dog clutch (8) when it is determined that the gradient of the clutch rotational speed difference [Delta]N is no longer decreasing.