Orthogonally-polarized dual-wavelength laser has significant practical applications in various fields, such as precision metrology, terahertz radiation generation, differential radar, spectral analysis. The Nd:YLF crystal has two orthogonally-polarized emission peaks with comparable emission cross sections, high-energy storage capability and relatively weak thermal lens effect. Owing to these properties, it has been recognized as a suitable gain medium for generating orthogonally-polarized dual-wavelength laser. In this paper, the Nd:YLF crystal with low doping concentration is employed as a laser gain medium to produce 1047 nm and 1053 nm dual-wavelength fundamental lasers with orthogonal polarizations, and the risk of thermal cracking of Nd:YLF crystal is reduced by appropriately increasing the pump spots. Using the intracavity Raman frequency shift in BaWO₄ crystal, orthogonally-polarized dual-wavelength Raman lasers at 1159.9 nm and 1167.1 nm are achieved to have high peak power. Under the total incident pump power of 40 W and a pulse repetition rate of 5 kHz, the maximum dual-wavelength Raman output power is obtained to be 2.67 W. The corresponding total optical conversion efficiency is 6.7%. For 1159.9 nm and 1167.1 nm Raman laser, their maximum average output power values are 1.31 W and 1.36 W, respectively. Their narrowest pulse widths are 1.50 ns and 1.53 ns, and the corresponding peak power values are as high as 174.7 kW and 177.8 kW, respectively. The results show that the problem of thermal cracking of Nd:YLF crystal at high pump power can be solved by reducing the doping concentration and increasing the pump spot. The Nd:YLF/BaWO₄ is a promising crystal combination for realizing orthogonally-polarized dual-wavelength Raman laser.