Image simulation for scanning transmission electron microscopy at atomic resolution for samples with realistic dimensions can require very large computation times using existing simulation algorithms. We present a new algorithm named PRISM that combines features of the two most commonly used algorithms, namely the Bloch wave and multislice methods. PRISM uses a Fourier interpolation factor f that has typical values of 4–20 for atomic resolution simulations. We show that in many cases PRISM can provide a speedup that scales with f4 compared to multislice simulations, with a negligible loss of accuracy. We demonstrate the usefulness of this method with large-scale scanning transmission electron microscopy image simulations of a crystalline nanoparticle on an amorphous carbon substrate.