A plastic upper jaw is pivotably mounted by a steel pin to a plastic base. A spring urges the jaw to close upon the base. A trigger is pivotably mounted to the base. A catch restrains the upper jaw in a set position until the trigger is actuated. The base has two upwardly extending side walls. Each side wall has a cable opening adjacent the floor of the base. A cable tie is looped around a pipe or support member and extends through the opposed openings in the opposite side walls. The ends of the tie are connected to secure the rodent trap to the support member. Because the upper jaw provides a wide gripping area, allowing the trap to be safely set, the trap is readily moved into the set position while it is secured to the support member, even if in an overhead position.