This paper reports the mechanism of hydrogen enrichment in stabilizing swirl/bluff-body CH4/air lean premixed flame. Large Eddy Simulation (LES) coupled with Thickened Flame (TF) model was performed to resolve the turbulent reacting flow. A detailed chemistry was used to describe the oxidization of CH4/H2/air mixtures. Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence of OH (OH-PLIF) simultaneous measurements were conducted to obtain the velocity fields and flame structures respectively. The numerical methods were validated by experimental data and showing good agreements. Both the experimental and numerical results show that, the flame brush attachment tends to leave the inner shear layer with increasing hydrogen addition, which will reduce the risk of flame lift-off. The chemical analyses prove that the attachment of CH4/air flame is inherently weak. On the one hand, the CH4/air flame is stabilized by the hot products inside the recirculation. On the other hand, the burnt gas suppresses the oxidation of H2 and CO through H2 + OH = H + H2O and CO + OH = CO2 + H, respectively. Although the proportion of CH4 decomposition through CH4 + OH = CH3 + H2O will be reduced by hydrogen addition, the path of CH4 + H = CH3 + H2 will be enhanced significantly. Hydrogen addition will not only increase the overall reaction rate, but also change the combustion intensity at the nozzle exit from relatively weak to strong, which is also important for flame stabilization. The robust flame attachment obtained by hydrogen addition can attributed to the enhanced reactions of H2 + OH = H + H2O and CH4 + H = CH3 + H2.