A lock structure of a connector includes a flexible lock arm, a lock engaging part and a releasing lever part. The flexible lock arm fixed to the second connector housing at a base end portion thereof is extended in a fitting direction of the connector. The lock engaging part provided at a distal end portion of the flexible lock arm is configured to be locked with a locking part provided in the first connector housing. The releasing lever part connected to the lock engaging part is extended along the flexible lock arm, and is configured to be rotated together with the lock engaging part around a pivot which is movable while releasing the lock. A thickness of the flexible rock arm is gradually decreased from the base end portion to the lock engaging part.