The Gibbs sampler has a great potential to be an efficient estimation procedure in item response theory. In this article, based on a data augmentation scheme using the Gibbs sampler, we propose a Bayesian

procedure to estimate the multidimensional grade response model with logistic link functions. The strategy is based on the Pólya–Gamma family of distributions which provides a closed-form posterior distribution for logistic-based models. With the introduction of the two latent variables, the full conditional distributions are tractable, and consequently the Gibbs sampling is easy to implement. Finally, the technique is illustrated by using simulated and real data, respectively.