Polarization effects on population transfer by stimulated Raman transition using overlapping time dependent pump and Stokes laser pulses from the ground X1Σg/+(vg=0, Jg=1) level of H2 to the final X1Σg/+(vf=1, Jf=1) level via the intermediate B1Σu/+(vi=14, Ji=0,2), C1Πu/+(vi=3, Ji=2) and C1Πu/−(vi=3, Ji=1) levels have been theoretically investigated by applying the density matrix formalism. We have studied in detail the dependence of the population transfer on time delay between two pulses for the cases of on-resonance excitations considering linear parallel and same-sense circular polarizations of the fields. The pump and Stokes fields are taken as having Gaussian pulse shapes with peak intensities IP/0(IS/0)=2 × 106 and 1 × 107 W/cm2. Density matrix equations have been solved for each value of the magnetic quantum number Mg(0, ±1) of the initial ground level taking into account the Mg dependence of the Rabi frequencies. Mg — averaged population transfer to the final level has also been calculated. For resonance excitations to the B(14, 0) or C(3, 1) levels, appreciable population transfer is achieved for intuitive pulse order for some particular values of Mg and Mi (magnetic quantum number of the resonant intermediate level) depending on the nature of polarizations. The calculated values of Mg — averaged population transfer for the two cases of polarizations show that for on-resonance excitation to the B(14, 0) or the C(3, 1) level, linear parallel polarization of the laser fields yield more transfer efficiency whereas for resonance excitation to the B(14, 2) level, larger population transfer results from the same-sense circular polarizations. For resonance excitation to the C(3, 2) level, Mg — averaged population is found to be almost polarization independent. The calculations for the six-level H2 system reveal some interesting features of polarization effects on the population transfer efficiency.