Investigates stochastic multi-criteria group decision making problems in which the criterion values are normal random variables and the criteria are in different priority levels. First, defines a new aggregation operator named normal distribution number prioritized weighted averaging (NDNPWA) operator and provides the relative properties of the operator. Furthermore, based on the NDNPWA operator and the normal distribution number weighted arithmetic averaging (NDNWAA) operator, proposes an approach for solving the stochastic multi-criteria group decision making problems in which the criterion values are normal random variables, the criteria are in different priority levels and the decision makers are not in different priority levels. Finally, presents an illustrative example to demonstrate the feasibility and effectiveness of the developed method.