Neutrinoless double-beta decay (0νββ) experiment searches for a minute peak next to the tail of 2νββ energy spectrum. This peak is hidden in thick and intricate backgrounds, thus hard to be perceptible. With no 0νββ signal excess over the background expectation yet, statistical limits are studied to describe the properties of 0νββ, based on the fitted background. In KamLAND-Zen experiment, the statistical limit of 0νββ rate is conventionally obtained by frequentist analysis. However, a Bayesian analysis can also extract the decay rate based on domain knowledge of double-beta decay model. A Bayesian analysis is presented here to independently compute and verify such a limit, contributing as a good complement and comparison study.