  In this work, we study charged current quasi elastic scattering of muon
anti-neutrino off nucleon and nucleus using a formalism based on Llewellyn
Smith (LS) model. Parameterizations by Galster et al. are used for electric and
magnetic Sach's form factors of nucleons. We use Fermi gas model along with
Pauli suppression condition to take into account the nuclear effects in
anti-neutrino - nucleus QES. We calculate muon anti-neutrino-p and muon
anti-neutrino-^{12}C charged current quasi elastic scattering differential and
total cross sections for different values of axial mass M_{A} and compare the
results with data from GGM, SKAT, BNL, NOMAD, MINERvA and MiniBooNE
experiments. The present theoretical approach gives an excellent description of
differential cross section data. The calculations with axial mass M_{A} = 0.979
and 1.05 GeV are compatible with data from most of the experiments.
