This article investigates the output fault-tolerant consensus problem for multi-agent systems with switching topology and deception attacks. In order to reduce the effects of switching topology, the differences between topologies can be modeled as topology uncertainties. In practice, the deception attack may occur in a random way and assumed to satisfy Bernoulli distributions. The purpose of this research is to design an output fault-tolerant controller such that, in the presence of switching topology, actuator faults, and deception attacks, the finite-horizon output fault-tolerant consensus can be achieved under a prespecified $$$ {H}_{\infty } $$$ performance. An initial-state-based performance requirement is constructed, and this bypasses the need for the zero initial condition in the conventional $$$ {H}_{\infty } $$$ theory. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed methods.