Distributed Denial of Service (DDoS) attack is the most common type of attack faced by today's data centers (DC). Such attacks can have a devastating impact on the system as it consumes resources like network bandwidth, hard disk storage, and CPU processing resources. As a consequence, the legitimate customers face more service blocking due to a major portion of the resources being occupied by the illegitimate traffic generated by the attackers. In this paper, we proposed a novel monitoring scheme based on the sliding window to detect and prevent the DDoS attack in DCs that serve enterprise customers that has low computational complexity. Compared to a benchmark scheme (without attack monitoring and preventing), our scheme ensures service provisioning for the legitimate customers with no false alarm. We also measure the robustness of our scheme in terms of the time taken to detect and prevent attack traffic by varying the traffic intensities of illegitimate traffic. Simulation results show that our scheme can successfully detect the attack even if the attack traffic intensity is not too much higher than the projected legitimate traffic intensity.