In order to predict the fuel consumption and carbon emission of vehicle driving on mountain city road, this research constructs energy conversion, fuel consumption and carbon emission model for N2 class heavy-duty diesel vehicle. The model is constructed based on the first law of engineering thermodynamics and the driving dynamic theory. The constructed model fully considers the impact of road slope characteristics on fuel consumption of mountain city roads and requires fewer parameters. The accuracy of the model is verified by actual road driving test data. Then, the prediction model is improved by adopting actual acceleration characteristics. Next, this research discusses the effects of speed, acceleration and slope on fuel consumption and carbon emission characteristics. Result indicates that when assuming the vehicle travels at a constant speed, the errors are large between measurement value and prediction value, the average errors are approximately 13% for fuel consumption and 14% for carbon emission. After considering the acceleration factor, the accuracy of the prediction model is significantly improved. Result shows that the correlation coefficient R2 between predicted value and tested value increased by 0.154 for fuel consumption and 0.183 for instantaneous work done, indicating an enhanced correlation between these values. This article constructs a vehicle fuel consumption and carbon emission model for mountain city roads. The predicted results of the model can reflect the actual fuel consumption and carbon emission levels during driving. Model developed in this paper has a typical physical meaning and can be applied to other roads and other vehicles.