This paper presented an energy-efficient adaptive cruise control, called Energy-Efficient Electric Driving Model (E3DM), for electric, connected, and autonomous vehicles (e-CAVs) in a mixed traffic stream. E3DM is able to maintain high energy efficiency of regenerative braking by adjusting the spacing between the leading and the following vehicles. Moreover, a power-based energy consumption model is proposed to estimate the on-road energy consumption for battery electric vehicles, considering the impact of ambient temperature on auxiliary load. Using the proposed energy consumption model, the impact of E3DM on vehicle energy consumption is investigated. In particular, single-lane vehicle dynamics in a traffic stream with a mixed of e-CAVs and human-driven vehicles are simulated. The result shows that E3DM outperforms existing adaptive cruise control (i.e. Nissan-ACC) and cooperative adaptive cruise control (i.e. Enhanced-IDM and Van Arem Model) strategies in terms of energy consumption. Moreover, higher market penetration of e-CAVs may not result in better energy efficiency of the entire fleet. The reason is that more e-CAVs in the traffic stream results in faster string stabilization which decreases the regenerative energy. Considering mix traffic streams with battery electric (BEVs) and internal-combustion engine (ICEVs) vehicles, the energy consumption of entire fleet reduces when the market penetration of BEV (contains both e-CAV and human-driven BEV) increases. A higher ratio of e-CAV to human-driven BEV results in higher energy efficiency.