Time-critical jobs in many real-time applications have multiple feasible intervals. Such a job is constrained to execute from start to completion in one of its feasible intervals. A job fails if the job remains incomplete at the end of the last feasible interval. This paper is concerned with how to find a schedule in which the number of jobs completed in one of their feasible intervals is maximized. We show that the maximization problem is NP-hard for both non-preemptible and preemptible jobs. This paper develops two approximation algorithms for non-preemptible and preemptible jobs. When jobs are non-preemptible, Algorithm LECF is with a 2-approximation factor; when jobs are preemptible, Algorithm LEF is proved being a 3-approximation algorithm. We also show that our analysis on the two algorithms is tight by providing a set of input instances. Simulation results demonstrate that Algorithms LECF and LEF not only guarantee the approximation factors but also outperform other multiple feasible interval scheduling algorithms.