  In this paper, we investigate a class of McKean-Vlasov stochastic
differential equations under L\'evy-type perturbations. We first establish the
existence and uniqueness theorem for solutions of the McKean-Vlasov stochastic
differential equations by utilizing the Euler-like approximation. Then under
some suitable conditions, we show that the solutions of McKean-Vlasov
stochastic differential equations can be approximated by the solutions of the
associated averaged McKean-Vlasov stochastic differential equations in the
sense of mean square convergence. In contrast to the existing work, a novel
feature is the use of a much weaker condition -- local Lipschitzian in the
state variables, allowing for possibly super-linearly growing drift, but
linearly growing diffusion and jump coefficients. Therefore, our results are
suitable for a wider class of McKean-Vlasov stochastic differential equations.
