Currently， there is a controversy about relationship between accuracies of Membership Inference Attacks （MIAs） in Generative Adversarial Networks （GANs） and generalization ability of the generative model itself， and thus effective attack ways are difficult to be widely applied， which limits the improvement of generative models. To solve the above problem， a Bayesian Estimation （BE）-based gray-box MIA scheme was proposed to match parameters in gray-box scenarios efficiently for optimal attacks. Firstly， training frameworks of the target and shadow models were designed under black-box conditions to obtain parameter knowledge required for the attack model. Then， the attack model was trained by combining and utilizing this effective parameter information to update the objective function continuously. Finally， the trained attack model was applied to MIA. Experimental results show that the attack accuracy of the gray-box attack scheme based on BE is improved by 15.89% and 21.64% respectively in average， compared to those of the existing white-box and black-box attack schemes. The above research achievements demonstrate a direct link between parameter exposure and Attack Success Rate （ASR）， and provide a direction for developing defensive strategies in this field.