In this paper, a novel and efficient analytical method is developed for evaluating the performance of threshold call admission policy for multi-class traffic in low Earth orbit mobile satellite systems. It eliminates the need of running very time-consuming and computationally intensive computer simulations as well as serves as the groundwork for developing performance optimization algorithms. The proposed analytical approach is based on a multi-dimensional Markov queuing model. Its effectiveness and accuracy have been validated by extensive computer simulations.