Summary: We give the structure of all covers of \(n\)-Lie algebras with finite dimensional Schur multipliers, which generalizes an earlier work of Salemkar et al. Also, for an \(n\)-Lie algebra \(A\) of dimension \(d\), we find the upper bound \(\dim{\mathcal M}(A) \leq \binom{d}{n}\), where \({\mathcal M}(A)\) denotes the Schur multiplier of \(A\) and that the equality holds if and only if \(A\) is abelian. Finally, we give a formula for the dimension of the Schur multiplier of the direct sum of two \(n\)-Lie algebras.