For a connected graph $G$ and $α\in [0,1)$, the distance $α$-spectral radius of $G$ is the spectral radius of the matrix $D_α(G)$ defined as $D_α(G)=αT(G)+(1-α)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. We give bounds for the distance $α$-spectral radius, especially for graphs that are not transmission regular, propose some graft transformations that decrease or increase the distance $α$-spectral radius, and determine the unique graphs with minimum and maximum distance $α$-spectral radius among some classes of graphs.