Nonlinear frequency upconversion of random fiber lasers can generate wavelength flexible visible light with low temporal coherence. In this work, we demonstrate wavelength-tunable blue light generation based on frequency tripling of a random Raman fiber laser (RRFL) in two cascaded periodically poled lithium niobate (PPLN) crystals. The RRFL can deliver watt-level and narrowband lasing in the spectral range of 1412-1435.5 nm, and by using a combination of a second-harmonic generation (SHG) and a sum-frequency generation (SFG) in two cascaded PPLN crystals, blue light with a spectral tuning range from 470.6 to 478.7 nm is experimentally achieved, which is the first demonstration, to the best of our knowledge, of visible light below 500 nm from the frequency conversion of random fiber lasers. Moreover, we confirmed that the temporal intensity fluctuations of the generated blue light are uncorrelated, making such a blue light source suitable for chaotic lidar and temporal ghost imaging applications. We believe the proposed frequency tripling of high-power and tunable RRFL can provide a new platform for generating wavelength flexible and temporal chaotic blue light, which can have promising applications in underwater lidar, display, and sensing applications.