Connectivity and automation provide a spectacular opportunity to improve traffic flow, safety, and efficiency due to their capability to exchange critical driving data and information. On the other hand, plug-in hybrid electric vehicles (PHEVs) have been a topic of extensive research in the past and it was demonstrated that it is a good solution for improving fuel economy and ecological features and their performance enhances with the addition of connectivity and automation. Coordination of vehicles at an urban area like roundabouts is a demanding problem especially by knowing that chance of both lateral and longitudinal collision exists. This paper proposes an approach for solving nonlinear multi-objective optimal control problem of decentralized coordination of connected and automated PHEVs (CA-PHEVs) at roundabouts with consideration of fuel economy. It was found that the proposed controller can calculate priority based on a navigation function and provide a safe gap between vehicles. Also, addition of energy cost to the performance index can improve the fuel consumption of the vehicle.