With the increasing popularity of photon-counting detectors in X-ray computed tomography, and with virtual clinical trials playing an increasingly important role in the evaluation of imaging systems, it is vital to have accurate simulation models for photon-counting imaging systems. Physical effects such as charge sharing, K-fluorescence and Compton scattering give rise to spatiotemporal correlations between different energy bins in different pixels, and existing methods for simulating such correlations accurately with multi-pixel correlation lengths are too computationally costly to be practical for full-size CT acquisition simulations. In this work, we propose a fast, accurate method for simulating correlated Poisson noise in photon-counting detectors based on the Anscombe transformation. We use Cholesky factorization to generate correlated Gaussian random numbers and then apply the inverse Anscombe transformation to map these into approximately Poisson-distributed counts. We show that any desired correlation structure of the counts can be obtained by adjusting the mean and covariance matrix used for the Gaussian random number generation. We evaluate this method in a simulation study with both a one-dimensional “toy” model with a single energy bin and a one-dimensional “realistic” model¹ , by using the chi-square statistic to assess the accuracy of the marginal probability distributions and pairwise joint probability distributions. The computational speed is compared to brute-force generation of Poisson random numbers. Our results show that the proposed method achieves reasonable accuracy in approximating the Poisson distribution, with > 80% lower chi-squared than a Gaussian approximation and that it can decrease the computation time to 1% of the time required for direct Poisson generation.