Spatial count data are observed in most sciences such as environmental sciences, meteorology, geology and medicine. To analyze count categorical data in which spatial correlation is observed, spatial generalized linear models based on Poisson (Poisson-lognormal spatial model) and binomial (binomial-logitnormal spatial model) distributions are often used. The likelihood function of these types of models has theoretical and computational complexities. A Bayesian approach using Markov chain Monte Carlo algorithms can be a solution for fitting these models, although there are usually problems in terms of low sample acceptance rates and long algorithm execution times. A suitable solution is to use the Hamiltonian Monte Carlo algorithm (hybrid) in the Bayesian approach. In this paper, a new Hamiltonian Monte Carlo method for Bayesian analysis of spatial counting models on Tehran city air pollution data is studied. Also, two common Monte Carlo algorithms, Markov chain (Gibbs and Metropolis-Hastings) and Langevin-Hastings, are used for full Bayesian approach of models on data. Finally, with diagnostic criteria, a suitable approach for data analysis and prediction in all parts of the city is introduced.