Pushback is a mechanism for defending against Distributed Denial-of-Service (DDoS) attacks. DDoS attacks are treated as a congestion-control problem, but because most such congestion is caused by malicious hosts not obeying traditional end-to-end congestion control, the problem must be handled by the routers. Functionality is added to each router to detect and preferentially drop packets that probably belong to an attack. Upstream routers are also notified to drop such packets in order that the router's resources be used to route legitimate traffic hence term pushback. Client puzzles have been advocated as a promising countermeasure to DoS attacks in the recent years. In order to identify the attackers, the victim server issues a puzzle to the client that sent the traffic. When the client is able to solve the puzzle, it is assumed to be authentic and the traffic from it is allowed into the server. If the victim suspects that the puzzles are solved by most of the clients, it increases the complexity of the puzzles. This puzzle solving technique allows the traversal of the attack traffic throughout the intermediate routers before reaching the destination. In order to attain the advantages of both pushback and puzzle solving techniques, a hybrid scheme called Router based Pushback technique, which involves both the techniques to solve the problem of DDoS attacks is proposed. In this proposal, the puzzle solving mechanism is pushed back to the core routers rather than having at the victim. The router based client puzzle mechanism checks the host system whether it is legitimate or not by providing a puzzle to be solved by the suspected host.