This paper is mainly concerned with fixed-time synchronization control for a class of Cohen–Grossberg neural networks (CGNNs) with nonlinear coupling and time-varying delay based on synchronization dynamics. First, by using a derived sufficient condition of fixed-time synchronization (FTS) for nonlinear coupled CGNNs (NCCGNNs) with time-varying delay, a novel fixed-time synchronization controller with time-varying delay is designed. Second, by combining the synchronization dynamic viewpoint and the obtained fixed-time synchronization control rule, several useful fixed-time synchronization controllers (FTSCs) are derived. Third, comparisons with known conclusions are provided to show the innovation and feasibility of the proposed fixed-time synchronization control methods. Finally, two examples are given to verify the effectiveness of the theoretical results. Compared with related works, the advantages of this paper are as follows: (1) The designed novel FTSCs can scientifically and efficiently process the time-varying delay of the addressed coupled CGNNs; (2) The derived settling time of the FTS built on FTSCs can reflect the effect of the proposed system’s parameters on the synchronization convergence time.