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Abstract Spin Hall oscillators (SHOs) based on bilayers of a ferromagnet (FM) and a non-magnetic heavy metal (HM) are electrically tunable nanoscale microwave signal generators. Achieving high output power in SHOs requires driving large-amplitude magnetization dynamics by a direct spin Hall current. Here we present an SHO engineered to have easy-plane magnetic anisotropy oriented normal to the bilayer plane, enabling large-amplitude easy-plane dynamics driven by spin Hall current. Our experiments and micromagnetic simulations demonstrate that the easy-plane anisotropy can be achieved by tuning the magnetic shape anisotropy and perpendicular magnetic anisotropy in a nanowire SHO, leading to a significant enhancement of the generated microwave power. The easy-plane SHO experimentally demonstrated here is an ideal candidate for realization of a spintronic spiking neuron. Our results provide an approach to design of high-power SHOs for wireless communications, neuromorphic computing, and microwave assisted magnetic recording.