For an intelligent hybrid electric vehicle (HEV), the economy‐oriented car‐following issue is a comprehensive problem of dynamic and economic performances, which involves in adaptive cruise control (ACC) and energy management strategy (EMS). In this study, three problems are formulated and analysed, which are a car‐following problem, HEV energy optimisation problem, and economy‐oriented HEV car‐following problem. In fact, the third problem includes the first and second problem. To describe the problems well, a novel efficiency model of HEV powertrain is proposed, and it is used to define the economic index for evaluation. The three problems can be solved by ACC, EMS, and combination of ACC and EMS. The comprehensive optimal solution for the third problem is analysed, which indicates that the fusion control is better than series control theoretically. Finally, a model predictive control method is used to compare the performances of fusion control with that of series control for a specific driving cycle. The results show that the fuel consumption of fusion control is less than that of series control by ∼5%.