In order to examine the validity of Wandzura-Wilczek relation for the polarized DIS structure function g 2 (x, Q 2 ), we use the light-front time-ordering pQCD to calculate g 2 (x, Q 2 ) at order α s on a quark target. We find that the study of the transverse polarized structure function in pQCD is only meaningful if we begin with massive quarks. The result shows that the Wandzura-Wilczek relation for g 2 (x, Q 2 ) is strongly violated by the quark mass in pQCD.