The chain recurrent set of an Anosov three-dimensional vector field (e.g. [3]) is an example of a non-transitive singular-hyperbolic attracting set containing hyperbolic repellers. Observe that this example has no singularities. In this paper we construct a C ∞ three-dimensional vector field that exhibits a singular-hyperbolic attracting set containing a singularity which is not Lorenz-like and a non trivial repeller hyperbolic set. © 2009 Pleiades Publishing, Ltd.