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A perfect matching in a graph $G$ is a set of nonadjacent edges coveringevery vertex of $G$. Motivated by recent progress on the relations between theeigenvalues and the matching number of a graph, in this paper, we aim topresent a distance spectral radius condition to guarantee the existence of aperfect matching. Let $G$ be an $n$-vertex connected graph where $n$ is evenand $\lambda_{1}(D(G))$ be the distance spectral radius of $G$. Then thefollowing statements are true.  \noindent$\rm{I)}$ If $4\le n\le10$ and ${\lambda }_{1} (D\left(G\right))\le{\lambda }_{1} (D(S_{n,{\frac{n}{2}}-1}))$, then $G$ contains a perfectmatching unless $G\cong S_{n,{\frac{n}{2}-1}}$ where$S_{n,{\frac{n}{2}-1}}\cong K_{{\frac{n}{2}-1}}\vee ({\frac{n}{2}+1})K_1$.  \noindent$\rm{II)}$ If $n\ge 12$ and ${\lambda }_{1} (D\left(G\right))\le{\lambda }_{1} (D(G^*))$, then $G$ contains a perfect matching unless $G\congG^*$ where $G^*\cong K_1\vee (K_{n-3}\cup2K_1)$.  Moreover, if $G$ is a connected $2n$-vertex balanced bipartite graph with$\lambda_{1}(D(G))\le \lambda_{1}(D(B_{n-1,n-2})) $, then $G$ contains aperfect matching, unless $G\cong B_{n-1,n-2}$ where $B_{n-1,n-2}$ is obtainedfrom $K_{n,n-2}$ by attaching two pendent vertices to a vertex in the$n$-vertex part.

Perfect matching and distance spectral radius in graphs and bipartite graphs