A continuous-wave (CW) single-longitudinal-mode (SLM) Raman laser at 1240 nm with power of up to 20.6 W was demonstrated in a free-running diamond Raman oscillator without any axial-mode selection elements. The SLM operation was achieved due to the spatial-hole-burning free nature of Raman gain and was maintained at the highest available pump power by suppressing the parasitic stimulated Brillouin scattering (SBS). A folded-cavity design was employed for reducing the perturbing effect of resonances at the pump frequency. At a pump power of 69 W, the maximum Stokes output reached 20.6 W, corresponding to a 30% optical-to-optical conversion efficiency from 1064 to 1240 nm. The result shows that parasitic SBS is the main physical process disturbing the SLM operation of Raman oscillator at higher power. In addition, for the first time, the spectral linewidth of a CW SLM diamond Raman laser was resolved using the long-delayed self-heterodyne interferometric method, which is 105 kHz at 20 W.