an arsenic tri-selenide-based strip/slot hybrid waveguide with a single horizontal silica slot is proposed to achieve an extremely low and flat dispersion with three zero dispersion wavelengths. by adjusting the geometrical structural parameters of the hybrid waveguide, dispersion tailoring is fully obtained. the flat group velocity dispersion varying between +/- 0.08 ps(2)/(m) is obtained over a 1253 nm bandwidth. the parameters of effective area, nonlinear coefficient, and third-order dispersion are all investigated. moreover, a compact on-chip all-optical wavelength converter is designed based on degenerate four-wave mixing in this waveguide. the dependencies of conversion efficiency and conversion bandwidth on the pump wavelength are discussed. the impact of pump power and signal power on the conversion efficiency is also investigated. the results show that a maximal conversion efficiency of 0.46 db, and a 3-db conversion bandwidth of 830 nm in the mid-infrared is achieved.