For the difference operator ∆m and the admissible ideal J ⊆ P(N), we aim in present work to introduce ∆m (J*N)-summability and ∆m (J*N)-summability in neutrosophic-n-normed linear spaces (briefly called N-n-NLS). We explore some basic properties of ∆m (J*N)-summability and ∆m (J*N)-summability and find conditions on J for which the two summability methods coincide. Finally, we define ∆m (JN)-Cauchy sequences in N-n-NLS and obtain the Cauchy convergence criteria.