A combination lock comprises a tumbler wheel assembly, a backup locking assembly comprising a keyhole, a shaft, and an inner projection having a half circular section, a pivot assembly having a dog and an engagement member, a push button secured to the pivot assembly, a U-shaped shackle pivotably fastened at the lock housing, and an L-shaped resilient member. A correct combination of tumblers and a subsequent pressing of the push button will disengage the dog from a slot at one leg of the shackle and thus exert an elastic force of the resilient member on the leg for pushing the leg out of engagement with the lock. Should either the combination be forgotten or the combination be changed by another person, a turning of the shaft about 90 degrees by inserting a key into the keyhole will turn the projection and the engaged engagement member for releasing the dog.