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The Protection Levels (PL) of Ground-Based Augmentation Systems (GBAS) are bounds of the positioning errors associated with given integrity levels. However, the practical Gaussian Overbounding Method (GOM) cannot describe the non-Gaussian nature of the error model such as “thick tail,” which makes PL tend to be overestimated. To overcome this problem, an error overbounding model based on stable distribution is proposed in this paper. Four stable distribution parameters are involved to accurately describe the GBAS ranging error. The weighted summation feature of the stable distribution is combined with the maximum likelihood estimation when calculating PL. Thus, it is possible to achieve a higher accuracy of PL under similar calculation complexity. In addition, this paper puts forward the Concept of Tightness (CoT) to describe the overbounding effect intuitively and quantitatively. In order to verify the effect of this method, multiple receivers are set to simulate the GBAS system, theyn the Stable Overbounding Method (SOM) is used to calculate the PL in two directions (Vertical and Lateral) under the hypotheses of H0 and H1. The CoT convincingly proves that the SOM has a better overbounding effect and improves the continuity of GBAS. It is evident that the multi-parameter SOM makes the overbounding of the protection level tighter and reduces the probability that the protection level is close to the Alarm Limit (AL), thus improving the accuracy of PL computing and the availability of GBAS systems.