For the scenario of heavy-duty vehicle driving on mountain city road, Support Vector Regression (SVR) model was proposed to be adopted to predict fuel consumption considering the strong generalization ability, simple structure, rigorous mathematical foundation and strong interpretability of the model. In response to the difficulty of parameters selection for SVR model, it was proposed to optimize the penalty factor (C) and kernel function parameter (sigma) of the SVR model using the Improved Grey Wolf Optimization algorithm (IGWO). Based on this, a prediction model for fuel consumption of heavy-duty vehicle driving on mountain city road based on the IGWO-SVR method was constructed. The SVR model optimized by the IGWO algorithm obtained a lower fitness value and the IGWO algorithm can obtain more accurate kernel parameter and penalty factor. For the IGWO-SVR model, when C is 169.6503 and sigma is 0.3391, the prediction model has the highest accuracy, with a fitness value (MSE) of 0.02319. Compared with PSO-SVR and GWO-SVR models, the IGWO-SVR model showed higher prediction accuracy and stronger generalization ability on all road sections. For suburban and highway sections, the R2 of the IGWO SVR model both reaches 95%. Finally, an energy-saving strategy for heavy vehicle climbing slope was proposed.