A centrifugal multistage pump that is characterized in that return vanes (6) are disposed in a return flow path (5) through which a fluid flows in a return direction toward a rotary shaft (2) and are arranged in the form of multiple circular cascades of vanes around the centerline (CL) of the rotary shaft (2) with the height of the return vanes (6) being aligned with the axial direction of the rotary shaft, the vane surface of each return vane (6) is formed into a curved surface that causes the direction of fluid flow in the return flow path (5) to change from the circumferential direction around the centerline (CL) to the radial direction toward the rotary shaft (2), and the camber lines (Ln1) of vane cross-sections (60c) of outer vanes (60) taken along a plane perpendicular to the axial direction of the rotary shaft (2) have different curved shapes when seen from the height direction, said outer vanes (60) being the vanes disposed on the most upstream side (Up) among the return vanes (6).