Formal methods have been widely used to support software testing to guarantee correctness and reliability. For example, model checking technology attempts to ensure that the verification property of a specific formal model is satisfactory for discovering bugs or abnormal behavior from the perspective of temporal logic. However, because automatic approaches are lacking, a software developer/tester must manually specify verification properties. A generative adversarial network (GAN) learns features from input training data and outputs new data with similar or coincident features. GANs have been successfully used in the image processing and text processing fields and achieved interesting and automatic results. Inspired by the power of GANs, in this paper, we propose a GAN-based automatic property generation (GAPG) approach to generate verification properties supporting model checking. First, the verification properties in the form of computational tree logic (CTL) are encoded and used as input to the GAN. Second, we introduce regular expressions as grammar rules to check the correctness of the generated properties. These rules work to detect and filter meaningless properties that occur because the GAN learning process is uncontrollable and may generate unsuitable properties for real applications. Third, the learning network is further trained by using labeled information associated with the input properties. These are intended to guide the training process to generate additional new properties, particularly those that map to corresponding formal models. Finally, a series of comprehensive experiments demonstrate that the proposed GAPG method can obtain new verification properties from two aspects: 1) using only CTL formulas and 2) using CTL formulas combined with Kripke structures.