We developed the quasi-particle random phase approximation (QRPA) for the neutrino scattering off even-even nuclei via neutral current (NC) and charged current (CC). The QRPA has been successfully applied for the β and ββ decay of relevant nuclei. To describe neutrino scattering, general multipole transitions by weak interactions with a finite momentum transfer are calculated for NC and CC reaction with detailed formalism. Since we consider neutron-proton (np) pairing as well as neutron-neutron (nn) and proton-proton (pp) pairing correlations, the nn + pp QRPA and np QRPA are combined in a framework, which enables 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 comply with other theoretical calculations and reproduce well available experimental data.