We developed the quasi-particle random phase approximation (QRPA) for neutrino reactions on even–even nuclei via neutral current (NC) and charged current (CC). The QRPA has been successfully applied for nuclear β and ββ decays. To describe neutrino–nucleus reactions, general multipole transitions by the weak interaction with finite momentum transfers are calculated for NC and CC reactions with detailed formulas. Since we consider neutron–proton (np) pairing as well as neutron–neutron (nn) and proton–proton (pp) pairing correlations, the nn+ pp QRPA and the np QRPA are combined in a framework, which enables us to describe both NC and CC reactions in a consistent way. Numerical results for ν–12 C,–56 Fe and–56 Ni reactions are shown to match with other theoretical calculations and well reproduce available experimental data.