In this paper, a new receding horizon control (RHC) scheme is proposed for a general class of uncertain linear systems with structured parametric uncertainties and linear input/output constraints. The cost function is defined over a moving finite horizon as the "worst-case" quadratic performance for all admissible uncertainties. The robust stability of proposed RHC scheme is guaranteed by imposing terminal penalty term using a control Lyapunov function (CLF), which is available through off-line synthesis procedure. Moreover, it is shown that the controlled performance of the proposed RHC scheme will be gradually improved as the upper bound of performance is monotonically decreasing as time goes by.