A copper alloy sliding bearing of a three-layer structure comprises a steel back metal layer of a high strength, a copper alloy layer, and an overlay. The steel back metal layer contains 0.15-0.26% by weight of carbon, and the steel back metal layer has a 0.2% yield strength of not less than 440 N/mm.sup.2. With this structure, even under severe conditions of use in an internal combustion engine of a high-speed design, in which an increased inertia force is applied to the housing, the followability of the bearing relative to the deformation of the housing is enhanced, and the bearing performance such as an anti-fretting property and an anti-seizure property is excellent.