A multiple-latch-locking lock structure includes a casing in which a lock tongue control unit and a lock latch control unit are arranged. The lock tongue control unit includes an operation-linking member, a positioning member, an arresting member, a swinging member, and a slide block. When a lock core is rotated, the rectangular lock tongue and the triangular lock tongue are driven to get pushed out and retracted back for latch-locking and unlocking. The lock latch control unit includes a rotating member, a slide plate, and a slide bar. When a handle is rotated, the lock latch is driven to get pushed out and retracted back, thereby achieving security latch-locking and the slide plate is caused to move up and down to achieve a function of controlling a vertical latch. As such, multiple latch locking can be achieved to provide the lock with better security and better burglary resistance.