Directly using brain signals rather than limbs to steer a vehicle may not only help disabled people to control an assistive vehicle, but also provide a complementary means of control for a wider driving community. In this paper, to simulate and predict driver performance in steering a vehicle with brain signals, we propose a driver brain-controlled steering model by combining an extended queuing network-based driver model with a brain-computer interface (BCI) performance model. Experimental results suggest that the proposed driver brain-controlled steering model has performance close to that of real drivers with good performance in brain-controlled driving. The brain-controlled steering model has potential values in helping develop a brain-controlled assistive vehicle. Furthermore, this study provides some insights into the simulation and prediction of the performance of using BCI systems to control other external devices (e.g., mobile robots).