The training of modern speech processing systems often requires a large amount of simulated room impulse response (RIR) data in order to allow the systems to generalize well in realworld, reverberant environments. However, simulating realistic RIR data typically requires accurate physical modeling, and the acceleration of such simulation process typically requires certain computational platforms such as a graphics processing unit (GPU). In this paper, we propose FRA-RIR, a fast random approximation method of the widely-used image-source method (ISM), to efficiently generate realistic RIR data without specific computational devices. FRA-RIR replaces the physical simulation in the standard ISM by a series of random approximations, which significantly speeds up the simulation process and enables its application in on-the-fly data generation pipelines. Experiments show that FRA-RIR can not only be significantly faster than other existing ISM-based RIR simulation tools on standard computational platforms, but also improves the performance of speech denoising systems evaluated on real-world RIR when trained with simulated RIR. A Python implementation of FRA-RIR is available online 1 .