Quasi-classical trajectory calculations for the reaction of Mg(3s3p(1)P(1)) with H-2 are performed on two potential energy surfaces (PES), the excited state (1)A' (or B-1(2) in the C-2v symmetry) in the entrance channel and the ground state (1)A' (or (1)A(1)) in the exit channel. A many-body expansion procedure is adopted for the construction of the analytical fit functions from the ab initio results. The title reaction involves a nonadiabatic transition between the two potential surfaces. For simplicity, the transition probability is assumed to be unity when the trajectory goes through the region of surface crossing and changes to the lower surface. The calculated total collisional deactivation and reaction cross sections decrease with the increase of translational collision energy. The calculated rotational product distributions are characterized by a bimodal feature both fur the MgH v = 0 and 1 states. The trend of bimodality is consistent with the observation reported in experimental studies. Our inspection of individual trajectories reveals that the low-rotational and high-rotational populations are caused by two distinct reaction pathways. This observation supports our previous expectation for the microscopic branching via the PES anisotropy. The angular product distribution indicates that the reaction proceeds predominantly via a linear collision complex. An increase of the collision energy from 2.026 to 8.104 kcal/mol has resulted in a shift of the distribution toward forward direction. The vibrational product distribution tends to decrease with the quantum numbers. The ratio of MgH(v = 1) to MgH(v = 0) yields a value of similar to 0.3, which is nevertheless underestimated as compared with the observation of 0.7 +/- 0.2. The reasons for the discrepancy are also discussed.