Failure detector is one of the fundamental building blocks to build reliable grid environments. There are large numbers of distributed applications with different QoS of failure detection in grids. Thus, in order to keep its efficiency and scalability in grid environments, a failure detector should not only provide QoS of accurate failure detection for applications, but also avoid redundant loads of designing multiple detectors for different QoS. Therefore, a new failure detector GA-FD (adaptive failure detector for grid) is presented, which adopts heartbeat detection strategy based on PULL mode. GA-FD can provide QoS of failure detection for multi-applications according to quantitative QoS metrics , and does not need any hypothesis about message behavior ),,(UMLMRUDTTTand clock synchronization. In addition, it proves that GA-FD implements a failure detector that belongs to ◇P in the partially synchronous model, and the experimental results are given in the end.