In the present paper, we introduce a new difference sequence space $r^q_B(u,p)$ by using the Riesz mean and the $B$-difference matrix. We show $r^q_B(u,p)$ is a complete linear metric space and is linearly isomorphic to the space $l(p)$. We have also computed its $\alpha$, $\beta$ and $\gamma$-duals. Furthermore, we have constructed the basis of $r^q_B(u,p)$ and characterize a matrix class $(r^q_B(u,p),l_\infty)$.