Partially missing or blurring attribute values make data become incomplete during collecting data. Generally we use inputation or discarding method to deal with incomplete data before clustering. In this paper we proposed an a new similarity metrics algorithm based on incomplete information system. First algorithm divided the data set into a complete data set and non complete data set, and then the complete data set was clustered using the affinity propagation clustering algorithm, incomplete data according to the design method of the similarity metric is divided into the corresponding cluster. In order to improve the efficiency of the algorithm, designing the distributed clustering algorithm based on cloud computing technology. Experiment demonstrates the proposed algorithm can cluster the incomplete big data directly and improve the accuracy and effectively.