In order to better solve the problem that the performance of failure detection is effected by dynamic of network environment in cloud computing, a new adaptive accrual failure detector (Two Windows Accrual Failure Detector, 2WA-FD) was proposed. First, two groups of actual data from two network conditions were analyzed, and we found that the Weibull distribution is a more reasonable distribution assumption for heartbeat inter-arrival time. According to the Weibull distribution, the suspicion level of accrual failure detector is more accurate. Second, the framework of accrual failure detector was analyzed and improved, and the suspicion level was calculated by two sliding windows. This framework is fit for dealing with the dynamic of network conditions. Finally, the 2WA-FD and other failure detectors were tested on open source experimental data and our experimental platform. The experimental results show that the 2WA-FD has better performance in terms of low detection time and high detection accuracy with the same detection overhead. Thus, the 2WA-FD can accurately and quickly find out the node failures in cloud computing, and effectively reduce the influence of dynamic on the performance of failure detection.