Beta regression models are useful for modeling continuous rates (proportions) affected by independent variables. Sometimes in the Bayesian inference of these models, the posterior distributions would not be constructed in closed form. Markov chain Monte Carlo algorithms for solving related integrals due to no small number of parameters may be time-consuming even faced with the problem of divergence. Using approximate Bayesian inference could be a solution for obtaining these posterior distributions. In this paper, the Bayesian Beta regression models are presented. The Integrated Nested Laplace Approximation will be offered for getting the posterior distributions in the analysis of these models. Moreover, these models' application is illustrated on a real data set.