When a vehicle travels on a road, different parts of vehicle vibrate because of road roughness. This paper proposes a method to predict road roughness based on vertical acceleration using neural networks. To this end, first, the suspension system and road roughness are expressed mathematically. Then, the suspension system model will identified using neural networks. The results of this step show that the neural networks model of suspension system will be well. The mean and max errors are 0.0013% and 0.0012, respectively. Finally, the inverse suspension system model is extracted by using neural networks to determine the relationship between road roughness and vibration or displacement. Using this step to predict the road quality. In this step, the mean error is 2.1% and max error is 0.028. Therefore, the results show that the proposed method can be used to identify the suspension system, inverse suspension system and predict the quality of roads.