With the consideration of personalized driving for automated vehicles (AVs), this paper presents a human-like decision making framework for AVs. In the modelling process, the driver model is combined with the vehicle model, which yields the integrated model for the decision-making algorithm design. Three different driving styles, i.e., aggressive, normal, and conservative, are defined for human-like driving modelling. Additionally, motion prediction algorithm is designed with model predictive control (MPC) to advance the effectiveness of the decision-making approach. Furthermore, the decision-making cost function is constructed considering drive safety, ride comfort and travel efficiency, which reflect different driving styles. Based on the decision-making cost function, a noncooperative game theoretic approach is applied to solving the decision-making issue. Finally, the proposed human-like decision making algorithm is evaluated with an overtaking scenario. Testing results indicate different driving styles cause different decision-making results, and the designed algorithm can always make safe and reasonable decisions for AVs.