Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erdős-Rényi random graph in large scale is often lack of local structure beyond the dyadic level and as a result we need to generate the clustered random graph instead of the simple random graph to compare the local structure at the triadic level. In this paper a generalized version of Gleeson's algorithm is advanced to generate a clustered random graph in large-scale which persists the number of nodes |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network. And it also has advantages in randomness evaluation and computation time when comparing with the existing algorithms.