The invention discloses a section assembly bridge girder erection machine suitable for a bridge with a small curve radius. The section assembly bridge girder erection machine structurally comprises amoving frame, a first support, a vehicle head, a vehicle compartment, a beam piece, a second support, a fine adjusting system and a third supporting frame. The vehicle compartment is mechanically connected with the vehicle head, a motor is arranged in the vehicle head, the first support is fixedly arranged on the vehicle compartment, and the movable frame is mounted at the top end of the first support. The section assembly bridge girder erection machine is provided with the fine adjusting system, a fine adjusting correction system, a step balancing structure and a counterweight system, the weight of a base is increased, the stability performance of the base is improved, the gravity center is lowered, meanwhile adjustment on the gravity center can be conducted according to the fine adjusting correction system, the section assembly bridge girder erection machine is suitable for any bridge, particularly overlapping joint of beam pieces of the bridge with the small curve radius, when the third supporting frame is unfolded and fixed, the base is stable, the gravity center is low, adding of assistance of external force is not needed, the fixing time is shortened, and the time cost is reduced.