The invention relates to a key-changeable lock including a lock housing and a lock cylinder provided within the lock housing. The lock cylinder includes a shell for the lock cylinder, a locking hole into which a key can be inserted and a locking block mounted on the shell. A sliding block and a toothed piece are provided in the shell. The locking block is abutted against the sliding block. Several toothed slides are slidably provided within the sliding block. The locking block can be located at two working positions. At a first working position, the locking block is not held in the block groove and the teeth of the toothed piece engage with those of the toothed slide. At a second working position, the locking block is held in the block groove and the teeth of the toothed piece disengage from those of the toothed slide.