This paper discusses stability of a load frequency control system with real-time pricing. The load frequency control system considered in this paper also depends on an external signal. The external signal corresponds to the predicted electrical load in spot pricing and is called as load-predicted signal. The load frequebcy control system with the external signal can be derived as an uncertain linear system. Since the uncertain linear system is described as an extended uncertain linear system which consists of monomials about the state, stability of the extened system is analized based on sum of squares. From the result of stability analysis, the admissible stability margin is obtained for the load-predicted signal. The efficacy of the load frequency control system with real-time pricing and load-predicted signal is demonstrated in a numerical example.