GAN-based tabular synthesis methods have made important progress in generating sophisticated synthetic data for privacypreserving data publishing. However, existing methods do not consider explicit attribute correlations and property constraints on tabular data synthesis, which may lead to inaccurate data analysis results. In this paper, we propose a Controllable tabular data synthesis framework with explicit Correlations and property Constraints, namely C3-TGAN. It leverages Bayesian networks to learn explicit correlations among attributes and model them as control vectors. Such control vectors can guide C3-TGAN to generate synthetic data with complicated property constraints. By conducting comprehensive experiments on 14 publicly available benchmark datasets, we showcase C3-TGAN's remarkable performance advantage over state-of-the-art methods for synthesizing tabular data.