This paper is concerned with H∞ control for a class of network-based T-S fuzzy systems with available asynchronous constraints on membership functions. Since a fuzzy controller in a network environment depends on available sampled-data measurements of premise variables and feedback states, the closed-loop system is represented by an asynchronous T-S fuzzy system with interval time-varying delay. Notice that the existing methods cannot be used to design the fuzzy controller for the closed-loop system because common product terms of membership functions in the asynchronous fuzzy system cannot be grouped. Instead, a novel fuzzy control design method is proposed by introducing upper bounds of asynchronous errors of membership functions with some free weighting matrices. New criteria on the existence of a network-based H ∞ controller are derived. The effectiveness of the proposed method is illustrated by a numerical example.