Low-loss depressed cladding waveguides have been produced in Nd:YAP laser crystal by using direct femtosecond laser writing. Under optical pump at 812 nm at room temperature, continuous-wave simultaneous dual-wavelength laser oscillations at 1064 and 1079 nm, both along TM polarization, have been realized in the waveguiding structures. It has been found that, with the variation of pump polarization, the intensity ratio of 1064 and 1079 nm emissions varies periodically, while the polarization of output dual-wavelength laser remains unchanged. The maximum output power achieved for the Nd:YAP waveguide lasers is ∼200 mW with a slope efficiency of 33.4%.