Conjugate prior density families were motivated by considerations of tractability in implementing the Bayesian paradigm. But we consider problem that the conjugate prior p($Theta$) cannot be used in restriction of the parameter $Theta$. This article considers the nonconjugate prior problem of hierarchical Poisson model. We demonstrate the use of latent variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate by using a Gibbs sampler.