Nonlinear frequency conversion plays a crucial role in advancing the functionality of next-generation optical systems. Portable metrology references and quantum networks will demand highly efficient second-order nonlinear devices, and the intense nonlinear interactions of nanophotonic waveguides can be leveraged to meet these requirements. Here we demonstrate second harmonic generation (SHG) in GaAs-on-insulator waveguides with unprecedented efficiency of 40 W$^{-1}$ for a single-pass device. This result is achieved by minimizing the propagation loss and optimizing phase-matching. We investigate surface-state absorption and design the waveguide geometry for modal phase-matching with tolerance to fabrication variation. A 2.0 $mu$m pump is converted to a 1.0 $mu$m signal in a length of 2.9 mm with a wide signal bandwidth of 148 GHz. Tunable and efficient operation is demonstrated over a temperature range of 45 $^{circ}$C with a slope of 0.24 nm/$^{circ}$C. Wafer-bonding between GaAs and SiO$_2$ is optimized to minimize waveguide loss, and the devices are fabricated on 76 mm wafers with high uniformity. We expect this device to enable fully integrated self-referenced frequency combs and high-rate entangled photon pair generation.
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