The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush. Intersection analysis, which identifies all pairs of intersected fractures (the basic components composing the connectivity of a network), is one of its crucial procedures. This paper attempts to improve intersection analysis through parallel computing. Considering a seamless interfacing with other procedures in modeling, two algorithms are designed and presented, of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy. A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations. Moreover, the preferred application conditions for the two algorithms are also discussed.