Recovering the ground motion time histories from the response spectra has potential utility in addressing earthquake engineering problems. However, the inverse mapping is challenging as the response spectra provide insufficient information to determine the corresponding time history. One possible solution is to utilize Generative Adversarial Networks (GANs), which are unsupervised deep learning algorithms capable of identifying intrinsic features of unlabeled data, enabling data augmentation. This study employed GANs to design a generator that can generate acceleration time histories covering long-term data variations with the input of pseudo-spectral acceleration (PSA) as a conditioning factor. The concept of Wasserstein GAN with gradient penalty (WGAN-GP) and Conditional GAN (CGAN) are combined for the purpose. The results of visual inspection and error metrics indicate that the PSAs of generated samples generally match the input PSA to the generator. The Arias intensities of generated samples typically exhibit similar trends with the measured attributes. Additionally, it was observed from the use of linear interpolation that the gradual changes of a latent vector to another selectively strengthen or weaken particular parts of the time history, leading to a gradual morphing of the overall shape of generated motions. The observation implies that the model generates samples by comprehending the underlying structure of data, as opposed to mere memorization.