A new London-Eyring-Polanyi-Sato (LEPS) potential energy surface (PES) is used in the O + CH4 -> OH + CH3 reaction via the quasiclassical trajectory method (QCT). Comparing with the experiments and the former ab initio calculations, the new LEPS PES describes the actual potential energy surface of the O + CH4 reaction successfully. The four polarization dependent "generalized" differential cross sections (PDDCS) are presented in the center of mass frame. In the meantime, the distribution of dihedral angle [P(phi(r)), the distribution of angle between k and j' (P(theta(r))] and the angular distribution of product rotational vectors in the form of polar plots in theta(r) and phi(r)(P(theta(r), phi(r)) are calculated. The isotope effect for the reactions O + CD4 is also calculated. These results are in good agreement with the experiments.