In order to alleviate traffic congestion for vehicles in urban traffic networks, many researchers have studied how to utilize the traffic resources such as roads effectively to supply effective route selection strategies for vehicles. Most of the current researches mainly focus on optimizing the signal cycle of traffic lights, supplying the optimized route selection for individual vehicles, and dispersing vehicles on the alternative routes based on their historical driving data or through the traffic game between the information center and the vehicles. However, the above methods have not considered the personalized traffic demands of each vehicle, the route selection conflicts between vehicles, or even the dynamic and uncertain traffic conditions in urban road networks. To solve these problems, this paper proposes a dynamic and real-time route selection model in urban traffic networks (DR²SM), which incorporates the preference for the alternative routes and the real-time traffic conditions. Through mutual information exchange, each vehicle uses a self-adaptive learning algorithm (SALA) to play the congestion game with each other to reach Nash equilibrium.