Superconducting radio-frequency cavities are commonly used in modern particle accelerators for applied and fundamental research. Such cavities are typically made of high-purity, bulk Nb and with cooling by a liquid helium bath at a temperature of ∼2 K. The size, cost and complexity of operating a particle accelerator with a liquid helium refrigerator make the current cavity technology not favorable for use in industrial-type accelerators. We have developed a multi-metallic 1.495 GHz elliptical cavity conductively cooled by a cryocooler. The cavity has a ∼2 µm thick layer of Nb3Sn on the inner surface, exposed to the rf field, deposited on a ∼3 mm thick bulk Nb shell and a bulk Cu shell, of thickness mm deposited on the outer surface by electroplating. A bolt-on Cu plate 1.27 cm thick was used to thermally connect the cavity equator to the second stage of a Gifford-McMahon cryocooler with a nominal capacity of 2 W at 4.2 K. The cavity was tested initially in liquid helium at 4.3 K and reached a peak surface magnetic field of ∼36 mT with a quality factor of 2 × 109. The cavity cooled by the cryocooler achieved a peak surface magnetic field of ∼29 mT, equivalent to an accelerating gradient of 6.5 MV m–1. The conduction-cooled cavity could be operated in continuous-wave with as high as 5 W dissipation in the cavity for 1 h without any thermal breakdown, because of the Cu outer layer with high thermal conductivity. This result represents a paradigm shift in the technology of superconducting accelerator cavities.