In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear discrete time-varying systems, which can be easily implemented by using linear matrix inequality (LMI) optimization. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix. The resulting stabilizing RHC scheme leads to time-varying finite terminal weighting matrices even for time-invariant systems, which is more general than in the case of using constant matrices. Based on the proposed scheme, another implementation method is also discussed for easy computation and numerical feasibility consideration of LMI optimization, although the second method does not guarantee the closed-loop stability theoretically. Through a simulation example, the effectiveness of the proposed schemes is illustrated.