The No-U-Turn Sampler (NUTS) is a relatively new Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior that common MCMC algorithms such as Gibbs sampling or Metropolis Hastings usually exhibit. Given the fact that NUTS can efficiently explore the entire space of the target distribution, the sampler converges to high-dimensional target distributions more quickly than other MCMC algorithms and is hence less computational expensive. The focus of this study is on applying NUTS to one of the complex IRT models, specifically the two-parameter mixture IRT (Mix2PL) model, and further to examine its performance in estimating model parameters when sample size, test length, and number of latent classes are manipulated. The results indicate that overall, NUTS performs well in recovering model parameters. However, the recovery of the class membership of individual persons is not satisfactory for the three-class conditions. Also, the results indicate that WAIC performs better than LOO in recovering the number of latent classes, in terms of the proportion of the time the correct model was selected as the best fitting model. However, when the effective number of parameters was also considered in selecting the best fitting model, both fully Bayesian fit indices perform equally well. In addition, the results suggest that when multiple latent classes exist, using either fully Bayesian fit indices (WAIC or LOO) would not select the conventional IRT model. On the other hand, when all examinees came from a single unified population, fitting MixIRT models using NUTS causes problems in convergence.