Clustering is a common technique for statistical data analysis and it has been widely used in many fields. When the data is collected via a distributed network or distributedly stored, data analysis algorithms have to be designed in a distributed fashion. This paper investigates data clustering with distributed data. Facing the distributed network challenges including data volume, communication latency, and information security, we here propose a distributed clustering algorithm where each IoT device may have data from multiple clusters. Considering that the main task of clustering is to compute each cluster center in a weighted averaging fashion, our distributed clustering method resorts to an efficient finite-time average-consensus algorithm. Experiments show that the proposed distributed clustering algorithm can offer the same convergence and clustering quality as its centralized counterpart but with less data traffic. Besides, experiments also show that our proposed algorithms outperforms the existing methods.