We present a continuously tunable high-power continuous wave (CW) single-frequency (SF) ${\text{Nd:YAlO}}_3$/lithium triborate (Nd:YAP/LBO) laser with dual-wavelength output, which is implemented by combining an optimized and locked etalon with an intracavity nonlinear loss. The obtained output powers of the stable SF 1080 and 540 nm lasers are 2.39 and 4.18 W, respectively. After the etalon is locked to an oscilating mode of the laser, the wideband continuous frequency tuning and long-term stable single-longitudinal-mode operation of the laser are successfully realized, which can be well used for the applications of quantum information and quantum computation. To the best of our knowledge, this is the first realization of the continuously tunable high-power CW SF 1080/540 nm dual-wavelength laser.