Inspired by the results of recent experimental discoveries for charm and bottom baryons, the masses and magnetic moments of the heavy baryons with J(P) = 3/2(+) containing a single heavy quark are studied within light cone QCD sum rules method. Our results on the masses of heavy baryons are in good agreement with predictions of other approaches, as well as with the existing experimental values. Our predictions on the masses of the states, which are not yet discovered in the experiments, can be tested in the future experiments. A comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is presented. (C) 2008 Elsevier B.V. All rights reserved.