A one-dimensional steady-state model for stimulated Raman backscatter (SRS) and stimulated Brillouin backscatter (SBS) processes in laser-irradiated plasmas is presented. Based on a novel “predictor-corrector” method, the model is capable to deal with broadband scattered light and inhomogeneous plasmas, exhibiting robustness and high efficiency. Influences of the electron density and temperature on the linear gains of both SRS and SBS are investigated, which indicates that the SRS gain is more sensitive to the electron density and temperature than that of the SBS. For the low-density case, the SBS dominates the scattering process, while the SRS exhibits much higher reflectivity in the high-density case. The nonlinear saturation mechanisms and competition between SRS and SBS are included in our model by a phenomenological method. The typical anti-correlation between SRS and SBS versus electron density is reproduced in the model. Calculations of the reflectivities are qualitatively in agreement with the typical results of experiments and simulations.