The object of the present paper is to study a type of contact metric manifolds, called 𝘕(𝑘)- contact metric manifolds admitting a non-null concircular and torse forming vector field. Among others it is shown that such a manifold is either locally isometric to the Riemannian product En+1(0) × Sn (4) or a Sasakian manifold. Also it is shown that such a contact metric manifold can be expressed as a warped product , where is a 2n-dimensional manifold.