Stimulated Raman scattering (SRS) is one of the main instabilities affecting the success of the fusion ignition. Here, we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations. The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated, which is consistent with our theoretical analysis quantitatively. Maxwellian distribution, flattened distribution, and bi-Maxwellian distribution are studied in detail, which represent three typical stages of SRS. We have also demonstrated the effects of plateau width, hot-electron fraction, hot-to-cold electron temperature ratio, and collisional damping on the Landau damping and growth rate. It gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.