This paper studies the leader-following consensus problem of discrete-time generic linear multi-agent systems. Agents share their states with their neighbors via a noisy communication network. An algorithm is proposed for the leader-following consensus problem where the time-varying gain is employed to attenuate noises. Different from most previous results where all agents have to use the same time-varying gain, each agent can have its own time-varying gain. Sufficient conditions for solving the mean square leader-following consensus problem are obtained: 1) the communication topology graph has a spanning tree; 2) the summation of every time-varying gain from zero to infinite is infinite; 3) all time-varying gains are infinitesimal of the same order as time goes to infinity; and 4) all roots of a so-called "parameter polynomial" are inside the unit circle. Finally, a simulation example is given to verify the theoretical results.