It’s of great value to analyze large-scale distributed graph statistics privately in nowadays. As an important structural statistic of distributed graph data, clustering coefficient is difficult to effectively collect because of its complex structural properties. The existing centralized nor local differential privacy (DP) based schemes cannot effectively solve the problems of third-party threats and low data utility, when estimating clustering coefficient. To this end, this paper proposes CC-SDP, a two-rounds interaction privacy-preserving scheme for estimating the clustering coefficient based on shuffled DP (SDP) in distributed settings. In this scheme, distributed users locally report local wedge lists of all edges by SDP and Random Response mechanism in first round and calculate local noisy triangle counts and degree values in the second round through Laplace mechanism; then the data collector estimates the global clustering coefficient by triangle count sequence and degree sequence. We provide specific steps of CC-SDP and demonstrate through theoretical analysis that CC-SDP satisfies to various DPs, with unbiased results. Experimental result shows that utilities of CC-SDP improved significantly than existing schemes based on local DP.