The key characteristics of two-lane-and-two-way traffic flow are platoon and overtaking caused by low-speed vehicle such as truck. In order to develop two-way traffic flow model comprised of CF(car-following) and overtaking model, it is essential to develop a car-following model which is suitable to two-way traffic flow. Short distance between vehicles is caused when a high-speed vehicle tailgates and overtakes foregoing low-speed vehicle on two-way road system. And a vehicle following low-speed vehicle decides to overtake the front low-speed vehicle using suitable space within the headway distribution of opposite traffic flow. For this reason, a two-way CF model should describes not only running within short gap but also headway distribution. Additionally considering domestic two-way-road size, there is a on-going need for large-network simulation, but there are few studies for two-way CF model. In this paper, a two-way CA model is developed, which explains two-way CF behavior more realistic and can be applied for large road network. The experimental results show that the developed model mimics stop-and-go phenomenon, one of features of congested traffic flow, and efficiently generates the distribution of headway. When the CF model is integrated with overtaking model, it is, therefore, expected that two-way traffic flow can be explained more realistically than before.