This research proposed an eco-driving system for an isolated signalized intersection under partially Connected and Automated Vehicles (CAV) environment. This system prioritizes mobility before improving fuel efficiency and optimizes the entire traffic flow by optimizing speed profiles of the connected and automated vehicles. The optimal control problem was solved using Pontryagin's Minimum Principle. Simulation-based before and after evaluation of the proposed design was conducted. Fuel consumption benefits range from 2.02% to 58.01%. The CO₂ emissions benefits range from 1.97% to 33.26%. Throughput benefits are up to 10.80%. The variations are caused by the market penetration rate of connected and automated vehicles and v/c ratio. No adverse effect is observed. Detailed investigation reveals that benefits are significant as long as there is CAV and they grow with CAV's market penetration rate (MPR) until they level off at about 40% MPR. This indicates that the proposed eco-driving system can be implemented with a low market penetration rate of connected and automated vehicles and could be implemented in a near future. The investigation also reveals that the proposed eco-driving system is able to smooth out the shock wave caused by signal controls and is robust over the impedance from conventional vehicles and randomness of traffic. The proposed system is fast in computation and has great potential for real-time implementation.