Summary: In this paper, we define and study Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces. Further, we consider finite-dimensional Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces and prove some theorems about completeness, compactness and weak convergence in these spaces. As an application, we get a stability result in the setting of Cheng-Mordeson \(\mathcal L\)-fuzzy normed spaces.