  In this paper, we are devoted to the numerical methods for mean-field
stochastic differential equations with jumps (MSDEJs). First by using the
mean-field It\^o formula [Sun, Yang and Zhao, Numer. Math. Theor. Meth. Appl.,
10 (2017), pp.~798--828], we develop the It\^o formula and construct the
It\^o-Taylor expansion for MSDEJs. Then based on the It\^o-Taylor expansion, we
propose the strong order $\gamma$ and the weak order $\eta$ It\^o-Taylor
schemes for MSDEJs. %We theoretically prove The strong and weak convergence
rates $\gamma$ and $\eta$ of the strong and weak It\^o-Taylor schemes are
theoretically proved, respectively. Finally some numerical tests are also
presented to verify our theoretical conclusions.
