The software quality model and software quality measurement model are the basis of evaluating the quality of the Foundational Software Platform (FSP), but it is quite difficult or even impossible to collect the whole metric data required in the process of the software quality measurement, which is the problem of the FSP quality evaluating. Bayesian networks are the suitable model of resolving the problem including uncertainty and complexity. By analyzing the problem domain of foundational software platform quality evaluation and comparing it with the characteristic domain of Bayesian networks, this paper proposed a method of evaluating the quality of the FSP by Bayesian network. The method includes three parts: node choosing, Bayesian network learning and Bayesian network inference. The results of the experiments indicate a Bayesian network for every quality characteristic should be built in practical quality evaluation of the FSP by the proposed method.