This paper investigates the second-order consensus problem for multi-agent systems with random link failures between each agent. The discrete-time multi-agent systems are described by the second-order dynamics, and the communication network is assumed to be directed with fixed topology. Since each link between the agents can be subject to failure with a certain probability, the control protocol is designed by considering the random link failures. The random link failures are presented by a Bernoulli probability sequence, that is, the control protocol for failure occurrence is designed by using the one step previous data that is sent by its neighbors' agents. The control protocol for second-order multi-agent systems is designed by using Lyapunov method. The mean square stability is shown for leaderless and leader-following multi-agent systems in terms of a set of linear matrix inequality (LMI), and some simulation results are provided to verify the effectiveness of the proposed methods.