The Internet is nowadays suffering dramatically serious attacks, with the distributed denial of service (DDoS) attacks being the representative and dominant ones. It is seen that, to stabilize the buffer queue length around a given target under DDoS attacks in the relevant routes is vitally important and helpful to mitigate the attacks and to improve the quality of service (QoS) for normal users. In the current paper, a stochastic queue dynamic model with L e ´ vy jump noise, which is affected by the continuous Brownian motion and the discontinuous Poisson process, is worked out to develop a novel and accurate mathematical framework for the stability of a route queue that deals with constant-rate DDoS attacks. This article proposes a security defensive mechanism in the network for solving the network collapse that can possibly be caused by DDoS attacks, otherwise. Particularly, based on the formulation of a stochastic queue dynamic with L e ´ vy jump noise, the mechanism that characterizes the behavior of the queue at routers is presented for stabilizing the queue length under constant-rate DDoS attacks. By applying the stochastic control theory into analyzing the performance of queue dynamic under constant-rate DDoS attacks, some explicit conditions are established under which the instantaneous queue length converges to any given target in a route. Simulation results demonstrate the satisfaction of the proposed defense mechanism with sharp contrast to the state of the art active queue management (AQM) schemes.