Functionalization of graphdiyne, a two-dimensional atomic layer of sp-sp(2) hybrid carbon networks, was investigated through first-principles calculations. Hydrogen or halogen atoms preferentially adsorb on sp-bonded carbon atoms rather than on sp(2)-bonded carbon atoms, forming sp(2)- or sp(3)-hybridization. The energy band gap of graphdiyne is increased from ~0.5 eV to ~5.2 eV through the hydrogenation or halogenation. Unlike graphene, segregation of adsorbing atoms is energetically unfavourable. Our results show that hydrogenation or halogenation can be utilized for modifying the electronic properties of graphdiyne for applications to nano-electronics and -photonics.