In this paper, we discuss the competition between the stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) instabilities under the strong damping condition. Based on a five-wave interaction model, relations of the stationary backscattering reflectivity between SRS and SBS are deduced in the case of homogeneous plasmas. Developments of the two coexistent instabilities are simulated with different parameters. The density and the temperature of plasma are found to be important in determining which instability dominates the backscattering in the regime of competition. Furthermore, the influence of inhomogeneous condition to the pattern of competition is analyzed. Numerical results consist with our theoretical results.