We introduce and study a new system of variational inclusions with ( H , η ) -accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the ( H , η ) -accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions in real q -uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.