To solve the short life time and low network throughput problems caused by the heterogeneity and mobility of Wireless Sensor Network (WSN) clustering algorithm, an Adaptive Clustering Algorithm based on Grades (ACA_G) was proposed. The proposed algorithm was run on rounds, which was composed of three stages:the adaptive clustering stage, the cluster construction stage and the data transmission stage. In the adaptive clustering stage, every partition may be subdivided or united adjacently according to the change of the number of nodes in each partition to keep an appropriate number of nodes in it. The adaptive clustering measure could be able to solve the unreasonable problems of the number of cluster-heads and the scale of clusters caused by the node mobility in WSN. In order to deal with the phenomena of some nodes died too fast and the life time of WSN was shortened caused by the heterogeneity in WSN, the node with the highest grade was selected as the cluster-head in the cluster construction stage. In the WSN application, the grade of each node was calculated according to the node residual energy, the speed of energy consumption, the distance between the node and the base station, the accumulated distance between the node and other nodes in the same cluster. The experiment was simulated by OMNeT++ and Matlab on a WSN with energy heterogeneity, in which node's mobile speed is 0~0.6 m/s randomly. The experimental results show that, compared with the Low Energy Adaptive Clustering Hierarchy -Mobile (LEACH-Mobile) algorithm and the Distributed Energy-Efficient Clustering (DEEC) algorithm, the life time of WSN clustered by the proposed algorithm is 30.9% longer than the other two algorithms, its network throughout is 1.15 times at least as much as the other two algorithms.