Time delays are widespread in power systems since communication networks can be used to send and receive information. In this paper, the influence of time-varying and constant delay on the stability of single area load frequency system is investigated. A comparative method to handle delay margins is presented. The maximum delay time when a power system is embedded into a steady state is treated as the delay margin of stability analysis. The main task of this paper is to calculate the upper bound of the maximal delay margin and reduce the conservatism of the previous methods. First, This paper investigates the stability about time-varying and constant delays of the LFC scheme based on linear matrix inequalities (LMIs) techniques. Second, a novel Lyapunov-Krasovskii function (LKF) is set up in which some new theories linked to the solving process of LKF. Finally, the superiority of the control method is verified by simulation.