This research focuses on the problem of operating system (OS) scheduling on asymmetric multi-core processors (AMP). A task scheduling model based on linear programming is proposed. Several attributes of AMP factors are taken into account in this model. Scheduling principles of behavior matching, migration avoiding, and load balancing are adhered as well. A comprehensive scheduling algorithm is also proposed based on the model. The algorithm has two parts: an integrated workload characterization, which proposes integrated behavior to measure the global and local behaviors of tasks comprehensively, and an integrated behavior- based scheduling algorithm, which efficiently utilizes the asymmetric multi-core processors without frequent task migration. This guarantees the load balance between cores. In addition, the algorithm achieves universality with a flexible parameter adjustment mechanism. It is an algorithm to achieve universality as well as the first to handle the global and local behaviors of tasks comprehensively. The evaluation on real platform demonstrates that the algorithm is universal for different conditions, and it always outperforms other scheduling algorithms on asymmetric multi-core processors (by 6%～22%).