Based totally on the intrinsic difference of polarizing emission spectra and birefringence of the a-cut Nd:YAP gain crystal, an orthogonally polarized 1079.5 and 1099 nm dual-wavelength laser is demonstrated. A specially designed dielectric Fabry-Perot filter is exploited as output coupler and gain balancer of the laser cavity. The maximum output power and slope conversion efficiency of the dual-wavelength laser is 976 mW and 7%, respectively. The experimental results show that the intrinsic birefringence of the laser gain material is the principle source for the generation of the orthogonal polarized laser. The competition between the two lasing wavelengths is analyzed and attributed to the stark energy levels involved. The method presented can be used to other biaxial laser gain crystals for the generation of orthogonal polarized dual-wavelength lasers.