Powertrain design undoubtedly plays an important role to improve the overall performance of the unprecedented rapidly developing Electric Vehicles (EVs) in recent years. Generally, parameters of the motor and transmission are the primary considerations to meet the performance requirements in electric vehicle design. However, the conventional powertrain design approach in most of the existing work limits the further improvements of the desired performances. In this work, the powertrain design and control problem of a 4-Independent-Wheel-Driving (4-IWD) electric race car with minimum lap time on a given circuit as evaluation criteria is investigated, based on a 7-DOF vehicle model. In particular, the investigated problem is formulated as an optimal control problem and solved with a software package GDYNOPT, taking into account the nonlinear load transfer and the powertrain mass variation that depends on the design parameters. At last, both the optimal design and control parameters are obtained at the same time.