Fuzzy C-Means (FCM) is susceptible to the influence of initial clustering centers, easy to converge to local optimum values and the inherent characteristics of daily load curve can not be fully reflected through distance when applied to clustering analysis of daily load curve. In order to solve the above problems, the dimensionality of daily load curve is reduced by using the characteristic value index of daily load. A fuzzy C-means clustering algorithm based on Grey Wolf Optimizer (GWO) optimization is proposed. The algorithm uses GWO to optimize the initial clustering center for FCM, and combines the global search ability of GWO and the local search ability of FCM. The results show that the proposed method can effectively improve the clustering effect of daily load curve and has good robustness. This work is supported by National Natural Science Foundation of China (No. 51777078) and Science and Technology Project of China Southern Power Grid Company (No. GDKJXM20172939).