When the smart grid phasor measurement equipment competes for limited network communication resources, the data packets will be delayed or lost due to uneven resource allocation, which will affect the accuracy of power system state estimation. To solve this problem, a Sampling Awareness Weighted Round Robin (SAWRR) scheduling algorithm was proposed. Firstly, according to the characteristics of Phasor Measurement Unit (PMU) sampling frequency and packet size, a weight definition method based on mean square deviation of PMU traffic flow was proposed. Secondly, the corresponding iterative loop scheduling algorithm was designed for PMU sampling awareness. Finally, the algorithm was applied to the PMU sampling transmission model. The proposed algorithm was able to adaptively sense the sampling changes of PMU and adjust the transmission of data packets in time. The simulation results show that compared with original weighted round robin scheduling algorithm, SAWRR algorithm reduces the scheduling delay of PMU sampling data packet by 95%, halves the packet loss rate and increases the throughput by two times. Applying SAWRR algorithm to PMU data transmission is beneficial to ensure the stability of smart grid.