In this paper, we characterize N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.We obtain some curvature properties. It is proven that if an N(κ)-contact metric manifold with generalized Tanaka-Webster connection is K-contact then it is an example of generalized Sasakian space form. Also, we examine some flatness and symmetric conditions of concircular curvature tensor on an N(κ)-contact metric manifolds with generalized Tanaka-Webster connection