In this paper, we present a novel framework for modeling Bayesian networks and performing quantitative Bayesian inference based on qualitative knowledge. Our method transforms qualitative statements into a set of structure and parameter constraints by making use of a proposed qualitative knowledge model. These qualitative constraints are utilized to restrain uncertainties in Bayesian model space and to generate a class of Bayesian networks which are consistent with the qualitative knowledge. Quantitative probabilistic inference is calculated by model averaging with Monte Carlo integration method. The method is benchmarked on ASIA network. Results suggest that our method can reasonably predict quantitative inference from a set of realistic qualitative statements.