In order to obtain an understanding of the relationship between the optical absorption and the transverse relaxation, the influences of linearly polarized light respectively at 133Cs D1 and D2 lines on the transverse relaxation of ground-state 133Cs atoms are studied. Under different vapor temperatures, light intensities and light frequencies, transverse spin relaxation times are separately measured for 133Cs atoms in different hyperfine levels. For theoretically analyzing the measuring results, especially for an unusual trend that the transverse spin relaxation time rises with the increase of light intensity, photon absorption cross-sections of linearly polarized light by 133Cs atoms are simulated. The experimental results show that through influencing the optical absorption and spin-exchange collisions, the linearly polarized light plays a remarkable role in the transverse spin relaxation. The results obtained by this paper can provide a guide to find the optimal intensity and frequency of linearly polarized light in practical applications for decreasing the influences of linearly polarized light on the transverse relaxation.