A two-stage torsion pivot hinge including an axle connected with a base and having a shaft mounted thereon with a bush for a spring tube. The bush forms a first and a second protrusion element respectively extending out of its two ends. The spring tube is fixedly connected with a supporting member and is provided with two torsion sleeves respectively on the two ends of the bush. Each torsion sleeve has an axial cut and has two contact elements extending respectively toward the two ends of the bush. The contact elements respectively interfere with the first and the second protrusion elements. By the function between the torsion sleeve and the bush, the pivot hinge can provide different torsion forces for the stroke of rotating the screen from its closed position to a vertical angular position and for the stroke from the vertical position to its maximum opening angular position.