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Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$s\left(L\right)=\frac{1}{2}(n-1)(n-2)+1-dimM\left(L\right)$$ where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.