The $D$-eigenvalues $\{\mu_1,\mu_2,\ldots,\mu_n\} $ of a graph $G$ are the eigenvalues of its distance matrix $D$ and form the $D$-spectrum of $G$ denoted by $spec_D(G)$. The $D$-energy $E_{D}(G)$ of the graph $G$ is the sum of the absolute values of its $D$-eigenvalues. We describe here the distance spectrum of some self-complementary graphs in the terms of their adjacency spectrum. These results are used to show that there exists $D$-equienergetic self-complementary graphs of order $n=48t$ and $24(2t+1)$ for $t\geq 4$.