An all-fiberized random distributed feedback Raman fiber laser (RRFL) with mode-modulation-induced wavelength manipulation and dual-wavelength generation has been demonstrated, where an electrically controlled intra-cavity acoustically-induced fiber grating (AIFG) is employed to adjust the input modal content at the signal wavelength. The wavelength agility of both the Raman effect and the Rayleigh backscattering in RRFL benefits on broadband laser output in case of broadband pumping. The feedback modal content at different wavelengths can be adjusted by AIFG, and then the output spectral manipulation can be ultimately manifested through the mode competition in RRFL. Under the efficient mode modulation, the output spectrum can be continuously tuned from 1124.3 nm to 1133.8 nm with single wavelength, while ulteriorly the dual-wavelength spectrum can be formed at 1124.1 nm and 1134.7 nm with a signal-noise-ratio of 45 dB. Throughout, the power is beyond 47 W with good stability and repeatability. To the best of our knowledge, this is the first dual-wavelength fiber laser based on mode modulation and the highest output power ever reported for an all-fiberized continuous wave dual-wavelength fiber laser.