Let $H$ be a spanning subgraph of $G$. If every vertex $v\in V(G)$ satisfies $a\le d_H(v)\le b$, then $H$ is called an $[a,b]$-factor of $G$. In 2005, Brouwer and Haemers pioneered the spectral approach for investigating $1$-factors in regular graphs. Since this work, adjacency eigenvalue conditions for $[a,b]$-factors have been extensively studied. In this paper, we provided some conditions based on the distance spectral radius that ensured the existence of an $[a,b]$-factor in a connected graph and a balanced bipartite graph, respectively.