A connector connection structure includes a first connector supported on a holder and a second connector connectable to the first connector. The holder has support portions in the form of U-shaped grooves, for supporting the first connector such that the first connector is slidable in a direction of connection of the first and second connectors relative to each other. Swingable levers are swingably supported between the holder and the first connector, and there are provided drive portions that swingingly displace the swingable levers in response to the sliding movement of the first connector. Operating portions are also provided to increase driving forces of the swingable levers, and transmit the driving forces to the second connector, thereby driving the two connectors in a direction to connect the two connectors together.