The invention relates to the recovery of heavy oil reservoirs, and more particularly to a supported catalyst-assisted microwave method for exploiting a heavy oil reservoir. The method includes: (1) injecting a slug of a supported catalyst fluid into the heavy oil reservoir; (2) placing a microwave generator in the heavy oil reservoir to perform volumetric heating on an oil layer containing the supported catalyst fluid; and (3) turning off the microwave generator and injecting water into the heavy oil reservoir for subsequent displacement, where a water injection rate is 3 m/d or less.