This invention discloses a lock that set on a suitcase of being opened or closed without using a zipper, which including an operating component and a locking component that are separately-mounted; the operating component is set on a non-border position of the suitcase, and the locking component is set on the border of the suitcase, wherein the locking component comprises at least one locking unit, the force transfer between the operating component and the locking component is provided by a force transmission mechanism that connected between the operating component and the locking component; the operating component comprises an operation member, and the locking unit comprises a lock head and a lock hook, wherein driving the operation member can drive the lock head or the lock hook to move through the force transmission mechanism, to lock or unlock the lock. This invention also provides a suitcase provided with the lock as described above. This invention set the operating component and the locking component separately, which solves the problem that the lock can only be installed on the border of the suitcase, and only the locking component needs to be installed on the border of the suitcase, while the operating component can be installed at any position of the suitcase other than the border.