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Cloud computing gets more and more popular because of its abilities on offering flexible dynamic IT infrastructure, QoS (Quality of Service) guaranteed computing environments and configurable software services. Cloud computing supports three service models: SaaS (Software as a Service), PaaS (Platform as a Service), and IaaS (Infrastructure as a Service). PaaS provides users with an application development and hosting platform with great reliability, scalability and convenience and it has many advantages in helping customers create applications compared with other service models. However, as a typical distributed system with limited computing resources, PaaS platform has to address the problems of resource management in order to achieve satisfactory QoS as well as efficient resource utilization. This paper presents an adaptive resource management algorithm called Feedback Control LRU (FC-LRU) which integrates the feedback control technique with LRU (Least Recently Used) algorithm. Simulation is conducted to evaluate the performance of FC-LRU and the results demonstrate that FC-LRU achieves satisfactory performance: it enables PaaS platform to maintain a low missed deadline ratio and high CPU utilization under the conditions of multitasks with different workloads.