Many population-based surveys have binary responses with covariates from individuals in each household (sub-area) within small areas. To make inference for the finite population proportion of individuals with a specific character in each household, we propose a Bayesian logistic regression model for sub-areas. The contribution of this model is twofold. First, we extend the integrated nested normal approximation (INNA) area level model to sub-area level model. This model is used to estimate small area means by borrowing strength from both related areas and sub-areas to obtain more precise sub-area estimators. Second, because there are numerous sub-areas, standard Markov chain Monte Carlo (MCMC) method to find the joint posterior density is very time consuming. But our model provides a sampling-based method that permits fast computation. Our main goal is to discuss this sub-area level hierarchical Bayesian logistic regression model and to show that it is much faster than the exact MCMC method and also reasonable. The performance of our method is studied by using the health status binary data for households (sub-areas) within wards (areas) in the Nepal Living Standard Survey II.