In order to ensure vehicle safety, enhance riding comfort, extend the battery life of electric vehicles (EVs), and improve the energy economy, an ADHDP-based economic adaptive cruise control (Eco-ACC) strategy for EVs in car-following scenarios is proposed in this paper. First, the longitudinal dynamics of EVs is modeled, and the control objectives are presented; then, the actor-critic structure of ADHDP is introduced, and the policy iteration formulas of the critic and actor networks in the ADHDP framework are given; finally, after the state variables, control variables, unity function and value function are determined, the ADHDP-based Eco-ACC strategy for EVs is designed. Extensive simulation results under different driving cycles show that the proposed Eco-ACC strategy can not only ensure vehicle safety, improve riding comfort and reduce energy consumption, but also significantly reduce the battery capacity loss and extend the battery life compared with the benchmark algorithm. In addition, the proposed Eco-ACC strategy is model-free and real-time, and can be robust in different car-following scenarios.