The time-dependent wave packet method is used to study non-adiabatic state-to-state Na(3p) + H-2(nu = 1, 2, 3, j = 0) -> NaH + H reactions, which are sub-processes in the formation of NaH from the collision between Na(3p) and H-2. Integral cross section values of the Na(3p) + H-2(nu) -> NaH + H reaction increase significantly when H-2 is excited to the nu = 2 or nu = 3 states. Products from the Na(3p) + H-2(nu) -> NaH + H reaction with three different initial vibrational states all prefer to form in vibrationally cold but rotationally hot states. Regarding the vibrational state distribution of the product from Na(3p) + H-2(nu > 0) -> NaH + H, our theoretical results are consistent with experimental results.