In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak-Orlicz function over n-normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over n-normed spaces. © 2018 World Scientific Publishing Company.