For a simple, undirected and connected graph $G$, $D_α(G) = αTr(G) + (1-α) D(G)$ is called the $α$-distance matrix of $G$, where $α\in [0,1]$, $D(G)$ is the distance matrix of $G$, and $Tr(G)$ is the vertex transmission diagonal matrix of $G$. Recently, the $α$-distance energy of $G$ was defined based on the spectra of $D_α(G)$. In this paper, we define the $α$-distance Estrada index of $G$ in terms of the eigenvalues of $D_α(G)$. And we give some bounds on the spectral radius of $D_α(G)$, $α$-distance energy and $α$-distance Estrada index of $G$.