Driver identification is an important research area in intelligent transportation systems, with applications in commercial freight transport and usage-based insurance. One way to perform the identification is to use smartphones as sensor devices. By extracting features from smartphone-embedded sensors, various machine learning methods can identify the driver. The identification becomes particularly challenging when the number of drivers increases. In this situation, there is often not enough data for successful driver identification. This paper uses a Generative Adversarial Network (GAN) for data augmentation to solve the problem of lacking data. Since GAN diversifies the drivers' data, it extends the applicability of the driver identification. Although GANs are commonly used in image processing for image augmentation, their use for driving signal augmentation is novel. Our experiments prove their utility in generating driving signals emanating from the Discrete Wavelet Transform (DWT) on smartphones' accelerometer and gyroscope signals. After collecting the augmented data, their histograms along the overlapped windows are fed to machine learning methods covered by a Stacked Generalization Method (SGM).The presented hybrid GAN-SGM approach identifies drivers with 97% accuracy, 98% precision, 97% recall, and 97% F1measure that outperforms standard machine learning methods that process features extracted by the statistical, spectral, and temporal approaches.