Six (1)A(') potential energy surfaces of the Ca+H-2 system have been calculated using an effective-core potential and a core-polarization potential for Ca. Large configuration interactions were performed to ensure accurate energies and wave functions. The 2 (1)A(') surface, made from Ca(4s3d, D-1), has a very stable intermediate, and crosses with the ground state (1 (1)A(')) potential energy surface in C-2v geometry. A diabatic coupling between these two can result in the CaH product. Three potential surfaces originating from Ca(4s3d, D-1) and two potential surfaces originating from Ca(4s4p, P-1) are well separated at low energy region, suggesting that the reaction product CaH from the Ca(4s4p, P-1) state via nonadiabatic transition to the Ca(4s3d, D-1) surface is very unlikely. Other possible routes of producing CaH from the Ca(4s4p, P-1) state also appear quite improbable in the single collision process. The wave function analysis does not show any sign of electron transfer from the metal atom to the hydrogen molecule in the reactant stage, which implies that the harpooning model does not apply to this reaction.