Acoustic simulation has always played an important role in the development of new ultrasound imaging techniques. In nonlinear ultrasound imaging particularly, the simulators are accurate but time-consuming, because of the high derivative order of the propagation equation and to the classic solution based on finite difference schemes. This article presents a fast 3D + t nonlinear ultrasound simulator, based on a generalized angular spectrum method, particularly fit for the graphics processing unit (GPU). Indeed, the Fourier domain approach decreases the derivative order of the propagation, thus significantly speeding up the simulation time. The simulator was implemented and optimized on a central processing unit (CPU) and a GPU, respectively. The processing times measured on two different graphic cards show that, compared to the CPU, GPU-based implementation is 3.5-13.6 times faster.