Effects of an external magnetic field on the excitation spectrum of the 15 V 31 344.9 band of the CS2 molecule are measured with sub-Doppler resolution. New lines ale observed to appear near the R(2) and P(4) lines when a magnetic field is applied. These lines are observed to be composed of five components both for the pi pump and for the sigma pump. From a theoretical analysis, we identify the new lines as transitions to the (3)A(2)(A(1)-B-1)(nu(-);12M) levels, which become allowed by Zeeman interaction with the V B-1(2)(nu’;03M) level that is mixed with the (3)A(2)(B-2)(nu;03M) level by spin-orbit interaction. Variations of energy shifts and intensities with the magnetic field strength are explained quantitatively by this analysis. M-dependent perturbation and the quenching of fluorescence are observed. The reason why large Zeeman splittings are observed at many lines in the V system of CS2 can be attributed to the spin-orbit interaction between the V B-1(2)(nu’;KJM) level and the (3)A(2)(B-2)(nu;KJM) level Combined with the rotational and/or the Zeeman interactions: : between (3)A(2)(B-2)(nu;KJM) level and either (3)A(2)(A(1)+B-1)(nu(0);K+/-1JM) or (3)A(2)(A(1)-B-1)(V-+/-;K+/-1J+/-1M) levels which are accidentally close in energy.