Compared with conventional spontaneous Raman scattering, stimulated Raman scattering (SRS) often uses two light fields (pump light and Stokes light), which provides an additional degree of freedom for polarization manipulation of SRS processes. A comparative study of SRS with circularly polarized and linearly polarized pump light field is carried out in this work. Firstly, based on the nonlinear coupled wave equation, the expressions of SRS signal intensity are derived theoretically under the cases that the pump light is circularly polarized and linearly polarized while Stokes light always keeps linearly polarized. And then, taking methane molecule with spherically symmetry as an example, the SRS spectra of υ₁ and υ₃ vibrational modes of methane molecule in the C-H stretching region (2800-3100 cm^-1) are experimentally measured under different polarizations. The experimental results are consistent with the theoretical analysis, demonstrating that the SRS signal intensity is not only closely related to the polarization state of pump light, but also to the symmetry property of molecular vibrational modes. The research provides useful insights for the polarization application of SRS.