The present paper introduces the generalized Riesz difference sequence space r(q)(B-u(p)) that consists of all sequences whose (RuB)-B-q-transforms are in the space l(p), where B stands for generalized difference matrix. Some topological properties of the new brand sequence space have been investigated as well as alpha- beta- and gamma-duals. In addition to this, we have also constructed the basis of r(q)(B-u(p)). At the end of the article, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.