Graph invariants, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. Recently, Gutman, Feng and Yu (Transactions on Combinatorics, 01 (2012) 27- 40) introduced the \emph{degree resistance distance} of a graph $G$, which is defined as $D_R(G)=\sum_{\{u,v\}\subseteq V(G)}[d_G(u)+d_G(v)]R_G(u,v)$, where $d_G(u)$ is the degree of vertex $u$ of the graph $G$, and $R_G(u,v)$ denotes the resistance distance between the vertices $u$ and $v$ of the graph $G$. Further, they characterized $n$-vertex unicyclic graphs having minimum and second minimum degree resistance distance. In this paper, we characterize n-vertex bicyclic graphs having maximum degree resistance distance.