The satellite-to-site visibility problem, which refers to the determination of opportunities for a satellite to observe or communicate with an object on the Earths surface, plays an important role in in the practical application of engineering. This paper presents a novel fast computation method for satellite-to-site visibility determination. The Radial-basis Functions (RBF) is utilized to approximate the discriminant function of the satellite-to-site visibility. Meanwhile, in order to improve the accuracy of the RBF, an adaptive interpolation method is used to generate more samples to construct the RBF approximation. The accurate rise and set times are obtained by solving a set of simply optimization problems about the RBF. To further increase the computational speed, an interval shrinking strategy is adopted via investigating the geometric relationship between the ground viewing cone and the orbit trajectory. Numerical results show a significant decrease in computation cost compared with the brute force method. In addition, the method is suitable for all orbital types and analytical orbit propagators.