A research has been conducted on a class of stability problems related to power load frequency sampling control systems with transmission delay taken into consideration. Firstly, a PI type LFC system scheme is adopted, followed by an establishment of a closed-loop LFC system model with sampling and transmission delay taken into consideration. Secondly, based on the established model, the delay stability margin of the system is calculated by using a criterion based on two-sided looped-functional, with a study on the relationship between the sampling period of the system and the delay stability margin, thus verifying the results through simulation by using a single region LFC system. The calculation results show that compared with existing literature, under the same system parameter conditions, there is a reduction in the conservatism of the results obtained by the proposed method, and the larger the sampling period, the smaller the stability margin of the system delay. A amount of time delay can increase the upper bound of the system sampling period. The simulation results further validate the effectiveness and advantages of the proposed method.