The origin of the p-type conductivity in N-doped ZnO has been a long standing puzzle for many years because isolated NO is considered to be a deep acceptor. Recently, the p-type doping has been attributed to the shallow acceptor NO−VZn complex that is supposedly being converted from a NZn−VO complex at the Zn-terminated surface [L. Liu et al., Phys. Rev. Lett. 108, 215501 (2012)]. By performing first-principles calculations, we demonstrate that the p-type NO−VZn pair is easy to form in bulk N-doped ZnO through the charge transfer and acceptor-acceptor level repulsion without the need of the special growth surface. More importantly, the NO−VZn pair can be further stabilized through hydrogenation, forming the more stable shallow acceptor complexes (NO−nH)−VZn (n=1−2) with an ionization energy of less than 162 meV, in good agreement with the experiment. These new shallow acceptor complexes are proposed to be responsible for the p-type conductivity of the N-doped ZnO.