Load curve clustering is a basic task for big data mining in electricity consumption. This paper proposed a clustering algorithm to improve the correct and accurate clustering of the load curve data. Firstly, we introduced the FastDTW as the similarity metric to measure the distance between two time series. Secondly, we used the Affinity Propagation (AP) to cluster. At last, we proposed a novel FastDTW-AP clustering algorithm for load curve clustering. As the similarity measures for clustering, we consider the Euclidean distance, Dynamic Time Warping (DTW), and Fast Dynamic Time Warping (FastDTW), and compare the efficiency of three similarity measures using the labelled dataset SCCTS from UCI. To evaluate the clustering algorithm, the real power load data is analyzed. The results show obvious improvement in evaluation index Adjust Rand Index (ARI) and Adjust Mutual Information (AMI).