The object of the present paper is to study N(k)-quasi-Einstein manifolds. Existence of N(k)-quasi Einstein manifolds is proved by a non-trivial example. Also some physical examples of N(k)-quasi-Einstein manifolds are given. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions C(ξ, X) · R = 0, R(ξ, X) · (formula present) = 0, and W (ξ, X) · S = 0, where R, C, (formula present) and S denote the Riemannian curvature tensor, the conformal curvature tensor, m-projective curvature tensor and Ricci tensor respectively. © 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.