As one of the significant enablers of portable devices and electric vehicles, lithium-ion batteries are drawing much attention for their high energy density and low self-discharging rate. A major hindrance to their further development has been the “range anxiety”, that fast-charging of Li-ion battery is not attainable without sacrificing battery life. In the past, much effort has been carried out to resolve such a problem by either improve the battery design or optimize the charging/discharging protocols, while limited work has been done to address the problem simultaneously, or through a control co-design framework, for a system-level optimum. The control co-design framework is ideal for lithium-ion batteries due to the strong coupling effects between battery design and control optimization. The integration of such coupling effects can lead to improved performances as compared with traditional sequential optimization approaches. However, the challenge of implementing such a co-design framework has been updating the dynamics efficiently for design variations. In this study, we optimize the charging time and cycle life of a lithium-ion battery as a control co-design problem. Specifically, the anode volume fraction and particle size, and the corresponding charging current profile are optimized for a minimum charging time with health-management considerations. The battery is modeled as a coupled electro-thermal-aging dynamical system. The design-dependent dynamics is parameterized thru a Gaussian Processes model, that has been trained with high-fidelity multiphysics simulation samples. A nested co-design approach was implemented using direct transcription, which achieves a better performance than the sequential design approach.