A random filtering decision-making method combining random simulation and filter analysis is proposed based on the basic assumption that each decision-maker's assessment information contains subjective and objective components. The mean value of objective component is used as ranking metrics, and the law of large numbers is employed to analyze its theoretical basis and physical significance. The convergence and advantages over other large group decision-making methods are also studied. The random empirical mode decomposition decision-making method is constructed, in which empirical mode decomposition is used as a filter method. An example is given to iaustrate the decision process, rationality and validity of the proposed method.