For $1{leq}k{leq}r$, let ${sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${sigma}({pi})$ = $d_1$ + $d_2$ + ${cdots}$ + $d_n;{geq};{sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r;{ imes};r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${sigma}$($K_{r,r}$ - ke, n) for even $r;({geq}4)$ and $n{geq}7r^2+{frac{1}{2}}r-22$ and for odd r (${geq}5$) and $n{geq}7r^2+9r-26$.