The structural and electronic properties of a heterojunction made of hexagonal boron nitride (h-BN) and g-C2N have been investigated by first-principles calculations involving the weak van der Waals (vdW) interaction described by the Grimme approach. It is found that the h-BN/g-C2N heterojunction is a typical type-II heterojunction with a direct band gap around 0.80 eV. The atomic projected density of states and the band-decomposed charge densities have demonstrated that the valence band maximum (VBM) and conduction band minimum (CBM) of the h-BN/g-C2N heterojunction are mainly provided by h-BN and g-C2N, respectively. Moreover, we find that the changes of band gap are very small for large variations of the vertical interlayer distance between h-BN and g-C2N. Our results indicate the great potential application in Li-ion battery and electronic device due to the large variation of interlayer distance induced by ion insertion or vertical strains for h-BN/g-C2N heterojunction.