We propose a widely tunable dual-wavelength Erbium-doped fiber laser that uses two micro-heater-integrated Fabry-Perot laser diodes (FP-LDs) and two fiber Bragg gratings (FBGs) for tunable continuous-wave (CW) terahertz (THz) radiation. Each wavelength can be independently tuned by using an FP-LD and an FBG. The wavelength fine tuning is achieved by simultaneously applying current to the micro-heater on the FP-LD and strain to the FBG. The side-mode suppression ratio is more than 35 dB for both wavelengths. The wavelength spacing of the dual wavelength can be continuously tuned from 3.2 nm to 9.6 nm. Continuous frequency tuning of the CW THz radiation is also successfully achieved using an InGaAs-based photomixer with our dual-wavelength fiber laser as the optical beat source. The emitted CW THz radiation is continuously tuned from 0.3 to 0.8 THz.