This paper addresses the design of a consensus-based asynchronous H∞ filter for a class of nonlinear discrete-time systems over a sensor network with switching topology. The filter structure includes both measurement update terms and a consensus term on the state estimates, and it is assumed to be asynchronously switched with the network topology. The time-delay approach is employed to stability and H∞ performance analysis of the filtering error system. The filter gains can be obtained based on the feasible solutions to a set of linear matrix inequalities. An example is provided to demonstrate the effectiveness of the proposed consensus-based filter design method.