A diode-end-pumped all-solid-state continuous-wave (cw) single-frequency tunable 1 542 nm laser is designed and fabricated. The laser oscillation at wavelength around 1 542 nm is realized by tuning the gain spectrum of the Er,Yb:YAB laser system via a special coating design. The cw single-frequency laser operation is achieved by using the twisted-mode technique for mode selection. Based on the optimization of the thickness of the gain medium and the transmission of the output coupler,the laser power is scaled up to 420 mW under 5.5 W pumping. The power stability of the laser is better than ±3％ during a given 3 hours. The laser intensity noise reaches the shot noise limit beyond the analysis frequency of 3 MHz. When an electro-optical crystal and an electro-optical etalon is inserted into the cavity and controlled by high voltage sources,quasi-wavelength-tuning of the cw single-frequency laser with the range of 1 541.959 nm~1 542.014 nm is demonstrated.