k-truss, a type of cohesive subgraphs of a network, is an important measure for a social network graph. However, with the emergence of large online social networks, the running time of the traditional batch algorithms for k-truss decomposition is usually prohibitively long on such a graph with billions of edges and millions of vertices. Moreover, the size of a graph becomes too large to load into the main memory of a single machine. Currently, cloud computing has become an imperative way to process the big data. Thus, our aim is to design a scalable algorithm of k-truss decomposition in the scenario of cloud computing. In this thesis, we first improve the existing distributed k-truss decomposition in the MapReduce framework. We then propose a series of theoretical basis for k-truss and use them to design an algorithm based on graph-parallel abstractions. Our experiment results show that our method in the graph-parallel abstraction significantly outperforms the methods based on MapReduce in terms of running time and disk usage.