Co-clustering on heterogeneous data has attracted more and more attention in web mining and information retrieval. The clustering approaches for two type heterogeneous data (bi-type co-clustering) have been well studied in the lit- erature. However, the work on data with more than two types (high-order co-clustering or multi-type co-clustering) is still limited. In this paper, we present a multi-type co- clustering algorithm, which clusters the data from differ- ent types simultaneously. We use a higher-order tensor to model the high-order relationships, each element of which describes the relation (similarity) among a given set com- posed by data objects from every types. Based on the high- order relationships, we embed the multi-type data objects into the low dimensional spaces by the algorithm based on Clique Expansion which can be viewed as a high-order extension of the normalized cut approach. At last, the k- means method is used to cluster the lower dimensional data. Experiment results show the effectiveness of the proposed method on both toy problem and real data.