All-solid-state continuous-wave (CW) single-frequency lasers have been established as efficient devices, capable of generating high stability, low intensity noise, and perfect beam quality. Among those lasers with diverse output wavelengths, the all-solid-state single-frequency lasers with the operating wavelength of 1.08 µm as promising light sources have been demonstrated to directly generate the continuous variable non-classical light fields by only utilizing one a-cut type-II non-critical phase-matching (KTP) crystal[2–6]. The achieved non-classical light fields act as the basic resources of the quantum computing (QC) and quantum information network (QIN). Therefore, the single-frequency CW 1.08 µm lasers can be broadly applied in quantum optics and quantum technologies. Moreover, because the wavelength of 1.08 µm corresponds to the cesium two-photon transition, the single-frequency 1.08 µm lasers can also be applied in atomic physics. In order to precisely match the cesium two-photon transition line, it is required to realize the frequency tuning of the single-frequency CW 1.08 µm lasers. In recent years, the Nd:CaYAlO4 (Nd:CYA) crystal as a candidate to emit the wavelength of the 1.08 µm laser has become more and more popular. In addition, several intrinsic advantages of the Nd:CYA crystal make it suitable for being used to generate the 1.08 µm lasers. Firstly, its absorption peak falls just around 807 nm (), which corresponds to the wavelength of the most mature laser diode (LD). Then, benefiting greatly from the disordered crystal structure[9,10], the Nd:CYA crystal has large inhomogeneous absorption (full width at half-maximum is 5 nm) and emission broadened spectra (full width at half-maximum is 20 nm). The spectral properties of the Nd:CYA crystal makes it a good candidate to attain tunable and ultrafast lasers. Owing to these desirable characteristics, a large number of CW transverse electromagnetic () mode lasers and tunable Q-switched lasers based on the Nd:CYA crystal have been studied. In 1989, Haracio et al. firstly, to the best of our knowledge, presented the laser action of Nd:CYA crystal and proved that CYA was a good host for rare-earth ions, and the maximum output power of the CW mode at 1.08 µm was about 80 mW. Stephens et al. further showed the continuous tunable single-mode laser of the Nd:CYA crystal from 1077.5 to 1084.5 nm with a Lyot filter in the resonator and the maximum output power with only 15 mW in 1992, which further confirmed that the emission spectra were broadened enough to be used for tuning and optically pumping metastable helium atoms. Yu et al. demonstrated a 5.16 W CW 1.08 µm laser with a Nd:CYA crystal and further obtained a passively Q-switched laser with a Cr:YAG in the cavity in 2010. In 2011, Fu et al. reported a CW frequency-doubled green laser at 540 nm in KTP crystal in a type-II phase-matching direction performed with a diode pumped Nd:CYA laser. The output power of 540 nm laser reached 324 mW, and its beam quality was 1.34 and 1.22 when the pump power was 18.2 W. Because of the multi-mode operation, there was cross saturation in the Nd:CYA crystal, sum frequency in the KTP crystal, and large fluctuation of the output power. However, up to now, there is no report on a stable CW single-longitudinal-mode (SLM) tunable laser based on Nd:CYA crystal, to the best of our knowledge. In this paper, we first, to the best of our knowledge, report a CW single-frequency tunable CW Nd:CYA laser with good performance. The output power of the single-frequency 1.08 µm laser reaches up to 1 W. The maximal and continuous tuning ranges of the 1.08 µm laser are up to 183.71 GHz and 60.72 GHz, respectively. The results prove that it can be an excellent source for QIN and QC.