In this paper, we propose a parameter identification method for stochastic biochemical reaction networks using flow cytometry data. A distinctive feature of the proposed method is that it is computationally efficient compared to existing works, thus it is applicable to complex biochemical networks. To this end, we first show that it is possible to construct a significantly small-order realization of the stochastic biochemical system using flow cytometry measurements. Then, the small-order realization is utilized for the development of the efficient identification method. Finally, the proposed method is demonstrated with an existing biological example.