The two characteristics of two-lane-and-two-way traffic flow are platoon and overtaking triggered by low-speed vehicle. It is crucial to develop a robust model which simultaneously generates the behaviors of platoon by low-speed vehicle and overtaking using opposite lane. Hence, a microscopic two-lane and two-way vehicle model was introduced (B. Yoon, 2011), which is based on CA (Cellular Automata) which is one of discrete time-space models, in Korea. While the model very reasonably explains the behaviour of overtaking low-speed vehicle in stable traffic flow below critical density, it has shortcomings to the overtaking process in unstable traffic flow above the critical density. Therefore, the objective of this study is to develope a vehicle model to more realistically explain overtaking process in unstable traffic flow state based on the model developed in the previous study. The experimental results revealed that the car-following model robustly generates the various macroscopic relationships of traffic flow generating stop-and-go traffic flow and the overtaking model reasonably explains the behaviors of overtaking under the conditions of both opposite traffic flow and stochastic parameter to consider overtaking in unstable traffic flow state. The vehicle model presented in this study can be expected to be utilized for the analysis of two-lane-and-two-way traffic flows more realistically than before.