Exploring new frequency bands for optical transmission is essential to overcome the capacity crunch. The 2-µm band is becoming a research spotlight due to available broadband thulium-doped fiber amplifiers as well as low-latency, low-loss hollow-core fibers. Yet most of the 2-µm band devices designed for optical communication are still in their infancy. In this Letter, we propose wavelength conversion based on four-wave mixing in a highly nonlinear AlGaAsOI nanowaveguide to bridge the 2-µm band and the conventional bands. Due to the strong light confinement of the AlGaAsOI nanowaveguide, high-order phase match is enabled by dispersion engineering to achieve a large synergetic conversion bandwidth with high conversion efficiency. Simulation results show a possible conversion bandwidth over an octave. An AlGaAsOI nanowaveguide with 3-mm length and a nominal cross-section dimension of $ 320\;{\rm nm} \times 680\;{\rm nm} $320nm×680nm is used for the wavelength conversion of a 10 Gbit/s non-return-to-zero on-off keying signal and a 10 Gbit/s Nyquist-shaped four-level pulse-amplitude modulation signal. A conversion efficiency of $ - {28}\;{\rm dB}$-28dB is achieved using a 17.5-dBm continuous-wave pump in the C band, with 744 nm conversion from 1999.65 to 1255.35 nm.