We demonstrate the high-power laser performance with a disordered Na:CaYAlO(4) crystal at a wavelength of about 1.08microm. Continuous-wave output power of 5.16W is achieved with a laser diode as the pump source. For the first time to our knowledge, the passively Q-switched Na:CaYAlO(4) laser is obtained with the maximum average output power of 2.39W, shortest pulse width of 5.7ns, and highest peak power of 15.47kW. By spectral analysis, the Nd:CaAlO(4) laser wavelength is centered at about 1.08microm. We propose that, by suitable tuning, the Na:CaYAlO(4) laser should be an excellent source for helium optical pumping.