In a scroll compressor furnished with a fixed scroll and an orbiting scroll, and provided with steps on end plates of the fixed scroll and the orbiting scroll, formed such that the height thereof is high at a central side and low at an outer peripheral end side in a spiral direction of the walls, and with upper rims of the walls formed in a stepped shape corresponding to the steps, gaps are respectively provided between the end plates and upper rims of the walls, and a height of the gaps at room temperature is formed higher than a height under operating conditions. Moreover, the steps are provided at positions which exceeds a pitch angle of &pgr; (rad) along the spiral direction from the outer peripheral end. Furthermore, a concavity is formed in the end plate of the fixed scroll, and a discharge valve is provided in the concavity. Moreover, a plate which is freely movable in an orbit axis direction of the orbiting scroll is arranged, and a pressing device which presses the plate is provided. In addition, a shape of connecting wall faces which connect adjacent parts on one side face of the end plates, is determined by an envelope drawn by an orbit locus of a connecting rim which connects adjacent parts of the upper rims. Furthermore, there is provided a communication passage which communicates between two compression chambers which are developed by contact of the connecting rim and the connecting wall face.