In this paper, we propose a generalized stabilizing receding horizon control (RHC) scheme for input and state constrained linear discrete-time systems, which includes existing ones, and is much more flexible and profitable in terms of feasibility and computation. The control scheme is based on a time-varying horizon cost function with time-varying terminal weighting matrices, which can easily be implemented via linear matrix inequality (LMI) optimization. We discuss modified schemes of the proposed one, which are better than the proposed general scheme in terms of feasibility or computation. Through various simulation examples, we illustrate the proposed results.