A set of vertices $W$ \textit{resolves} a graph $G$ if every vertex in $G$ is uniquely determined by its vector of distances to the vertices in $W$. \ The \textit{metric dimension }of $G$ is the minimum cardinality of a resolving set of $G$. \ For $n\geq 3$, an $n$-complete partite graph $G(k_1, k_2, ..., k_n)$ is a graph whose vertex set $V$ can be partitioned into $n$ subsets $V_1, V_2, ...,V_n$, with $|V_i|=k_i \geq 3$, such that every edge of $G(k_1, k_2, ..., k_n)$ joins $V_1, V_2, ...,V_n$. \ Recently, we have determined the metric dimension of regular bipartite which is isomorph to a complete bipartite graph minus a perfect matching (Baca \emph{et al.}, Bull. Math. Soc. Sci. Math. Roumanie, $2011$). \ Continuing our previous results, in this paper we determine the metric dimension of $G(k_1, k_2, ..., k_n)$ minus a perfect matching.