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Let $G$ be a connected graph with vertex set $V\left(G\right)=\{v_1,v_2,...,v_n\}$. The distance matrix $D\left(G\right)={\left(d_{ij}\right)}_{n\times n}$ is the matrix indexed by the vertices of $G$, where $d_{ij}$ denotes the distance between the vertices $v_i$ and $v_j$. Suppose that ${\lambda }_1\left(D\right)\ge {\lambda }_2\left(D\right)\ge \cdots \ge {\lambda }_n\left(D\right)$ are the distance spectrum of $G$. The graph $G$ is said to be determined by its $D$-spectrum if with respect to the distance matrix $D\left(G\right)$, any graph having the same spectrum as $G$ is isomorphic to $G$. We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined...