In this paper we introduce the notion of $\mathcal{I}_{\lambda}-$statistical convergence of sequences as one of the extensions of $\mathcal{I}-$ statistical convergence in the gradual normed linear spaces. We investigate some fundamental properties of the newly introduced notion and its relationship with $\mathcal{I}-$ statistical convergence. In the end, we introduce and investigate the concept of $\mathcal{I}_{\lambda}-$statistical limit points, cluster points and establish some implication relations.