The invention provides a steel pipe loading and unloading crane and a construction method of the steel pipe loading and unloading crane. The steel pipe loading and unloading crane comprises a movable portal. A beam is arranged on the top of the portal. A crane trolley is arranged on the beam. The crane trolley can be adjusted and move in the length direction of the beam. A hoisting main arm capable of ascending and descending is mounted on the crane trolley. An extending-and-contracting steel pipe bracket for bearing steel pipes is arranged on the hoisting main arm. A hoisting claw for grabbing the steel pipes is arranged on the steel pipe bracket. The hoisting claw can be adjusted and move in the extending-and-contracting direction of the steel pipe bracket. The steel pipe loading and unloading crane and the construction method solve the problem that an existing door-opening type container is difficult to load and unload, the labor intensity of workers is further lowered, the loading and unloading efficiency is improved, and the potential safety hazards of construction are avoided.