The g-factors of the 2 3P, 2 1P, and 3 3P states of the helium atom are calculated by using the vatiational wave functions constructed from the linear combinations of Slater-type basis sets. The relativistic corrections to order α 2(a.u.) and the effect of the motion of the center of mass are treated by using first-order perturbation theory. Most of our predicted results are in good agreement with recent results of Yan and Drake, which were obtained by using the wave functions with doubled Hylleraas coordinates. Based on the analysis of the convergence pattern in our calculation, we believe that our predicted value of the δg L-factor for 3 3P state in 4He, 2.914 15×10 -7,ought to be reasonable and accurate, although there are no corresponding experimental data available in the liteature yet to be compared with.