Although many applications involve autocorrelated multivariate counts, there is a scarcity of research on their statistical modeling. To fill this research gap, this article proposes a state space model to describe autocorrelated multivariate counts. The model builds upon the multivariate log-normal mixture Poisson distribution and allows for serial correlations by considering the Poisson mean vector as a latent process driven by a nonlinear autoregressive model. In this way, the model allows for flexible cross-correlation and autocorrelation structures of count data and can also capture overdispersion. The Monte Carlo Expectation Maximization algorithm, together with particle filtering and smoothing methods, provides satisfactory estimators for the model parameters and the latent process variables. Numerical studies show that, compared with other state-of-the-art models, the proposed model has superiority and more generality with respect to describing count data generated from different mechanisms of the process of counts. Finally, we use this model to analyze counts of different types of damage collected from a power utility system as a case study. Supplementary materials are available for this article. Go to the publisher’s online edition of IISE Transactions for additional tables and figures.