Failure detection provides the ability of timely detecting the liveliness of runtime systems and is the basic reliability technology in distributed systems. Providing good failure detection is important to Web application server (WAS) that is the leading middleware in Web computing environment. Adaptive failure detection requires that failure detectors can dynamically adjust the detecting quality according to the requirements of applications and runtime environments. In this paper, the concepts and qualities of failure detectors are firstly discussed, and a multi-level model of failure detection in WAS is presented. Based on the QoS (quality of service) specification of failure detectors, an algorithm for adaptive failure detection is given, and an adaptive failure detection framework of WAS is designed, which can satisfy the requirements of dynamically adjusting qualities and flexible integration of failure detectors. The work has been implemented in OnceAS application server, and the experimental results are given in the end.