A scroll compressor comprises a fixed scroll member and a revolving scroll member that engage with each other with their centrifugal walls, wherein the revolving scroll member is supported to revolve with respect to the fixed scroll member, but to avoid self-rotation thereof. The spiral-starting portion of the centrifugal wall comprises non-stepped portions formed along curves of &bgr;1-&bgr;1′ and &bgr;2-&bgr;2′ respectively, and a stepped portion formed along a curve &bgr;1′-&bgr;2′ that provides a thickness increase area encompassed by its upper-side curved surface and its lower-side curved surface. The discharge port is located on the end board of the fixed scroll member to partly overlap with the thickness increase area by partly hollowing the lower side of the stepped portion with the prescribed height.