This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets, The control scheme for the underlying systems is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix at each time instant, This robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters. The proposed controller is obtained using semidefinite programming.