PROBLEM TO BE SOLVED: To provide a multistage centrifugal fluid machine in which an influence of a leakage flow on a main flow is reduced to improve its performance.SOLUTION: A multistage centrifugal fluid machine includes: a rotating shaft 4 rotated around an axis 0; multistage impellers 6 for flowing out a major flow WO of a fluid W flowing from a direction of the axis 0 into an inlet from an outlet toward an outside in a radial direction through rotation together with the rotating shaft 4; an internal casing 3 covering the rotating shaft 4 and the multistage impellers 6 to define flow passages 7 through which the major flow WO flowing into each of the impellers 6 flows; and steps 32 arranged at connected portions with flow passages 7 as outlets of a clearance S (a leakage flow path) formed between a cover 20 for each of the impellers 6 and the internal casing 3 so as to protrude from the internal casing 3 toward the cover 20, and with which a leakage flow W1 flowing in the clearance S along the axis 0 dire
