Computational models of driving behavior developed in a cognitive architecture can provide better scientific understanding of driving, simulate driving behavior, quantitatively predict possible interference of in-vehicle tasks, and thus help develop human factors guidelines and tools for in-vehicle systems design. Driver lane changing is a common activity in driving. Therefore, modeling driver lane changing control with a cognitive architecture should be an important component of cognitive models of driving behavior. In this paper, we develop a computational model of driver lane changing control with the Queuing Network-Model Human Processor (QN-MHP) cognitive architecture based on neuroscience and psychological findings. The simulation and experimental results from lane changing on straight and curved roads show that this model can perform the control process of lane changing well and the model's control process is consistent with that of drivers.