A narrow linewidth and wideband tunable continuous-wave terahertz generator with DAST crystal has been demonstrated in this paper. Two narrow-linewidth CW fiber lasers were used as the pump sources for difference frequency generation. The terahertz wave can be continuously tunable in the range of 1.1-3 THz. The maximum output power of 2.79nW was obtained at 2.568 THz. The linewidth of the output THz wave was estimated to be 56.5 MHz by fitting transmission spectrum of CO gas at 450 Pa pressure around 80.52 cm-1 with the Vogit gas model. Furthermore, the output spectra at room temperature and pressure was in good agreement with the air absorption lines in Hitran database. Moreover, the narrower absorption characteristic spectrum of 2-Deoxy-D-Glucose sample has been obtained through the spectrum measurements. Therefore, it could promote the practical prospect of tunable CW-THz source, which will have good potential in THz high-precision spectroscopic detection and multispectral imaging.