This paper addresses the mean square consensus problems for leader-following multi-agent systems under denial-of-service(DoS) attacks, process noise and measurement noise. Firstly, a state observer is presented to estimate the state of each agent effectively and accurately. Then, based on the predictive control theory, a distributed predictive control protocol based on the state estimation information of each agent is proposed for the leader-following multi-agent systems to achieve mean square consensus. Sufficient and necessary conditions of consensus for the leader-following multi-agent systems under DoS attacks are derived. Finally, a numerical example is provided to verify the correctness and effectiveness of the proposed methods.