A clamping apparatus of an injection molding machine is provided. A first driving device operates a movable platen to perform mold opening/closing. A second driving device applies a clamping force to the movable platen. A screw mechanism converts rotational power of the driving devices into linear power. By contact/separation between a first rotation plate coupled to a screw shaft and a second rotation plate, a power transmission device switches transmission of power from the second driving device to the screw mechanism. At the normal time, an urging mechanism integrally moves the screw shaft and the first rotation plate in a mold closing direction and releases the connection of the second driving device. When the mold closing is completed, the urging mechanism allows the screw shaft and the first rotation plate to integrally move in a mold opening direction, and brings the second driving device into a connected state.