Car-sharing companies have shown increasing support in the adoption of fuel-efficient cars to reduce CO2 emissions and to meet heterogeneous demand. In this paper, we consider location design and relocation problems for sharing a mixed fleet of cars and propose integer linear programs that incorporate both one-way and round-trip demand and operations. To model car movements, we use a minimum-cost flow model on a spatialtemporal network given time-based demand. We maximize the total profit of renting cars minus the cost of relocation and maintenance, subject to limited budget for purchasing cars and given a CO2 emission limit. In addition, we enforce the first-come, first-served principle to eliminate denied trips. We conduct computational studies based on 2014 Zipcar data in Boston to provide insights for fleet location, car-type designs, and their environmental impacts. Our results show high utilization of cars and low demand losses and denied trips. Although the CO2 emission limit may lower car-sharing profit, high demand on new energy-efficient cars can compensate the loss and is worth being satisfied.