In this technical note, the consensus control problem is investigated for a class of discrete time-varying stochastic multi-agent system subject to sensor saturations. An event-based mechanism is adopted where each agent updates the control input signal only when the pre-specified triggering condition is violated. To reflect the time-varying manner and characterize the transient consensus behavior, a new index for mean-square consensus is put forward to quantify the deviation level from individual agent to the average value of all agents' states. For a fixed network topology, the aim of the proposed problem is to design time-varying output-feedback controllers such that, at each time step, the mean-square consensus index of the closed-loop multi-agent system satisfies the pre-specified upper bound constraints subject to certain triggering mechanism. Both the existence conditions and the explicit expression of the desired controllers are established by resorting to the solutions to a set of recursive matrix inequalities. An illustrative simulation example is utilized to demonstrate the usefulness of the proposed algorithms.