In this paper, asymptotic stability theorems for zero solutions of a class of nonlinear multivariate time-lagged generalized Halanay inequalities are given using the fixed point method. This study is an attempt of the fixed point method in the study of the stability of Halanay inequalities, and the results show that the use of the fixed point method to study the stability of Halanay inequalities has certain superiority compared with other methods in certain situations. According to the different characteristics of time lag system coefficients, the proof process of this paper introduces the corresponding functions to construct the operator, which makes the conclusion more flexible and feasible. After that, the obtained results are applied to study the stability of neural network systems in this paper, and better conclusions are obtained. The numerical simulation results combined with the cases verify the accuracy and superiority of the conclusions of this paper. This study adds new methods and new ideas to the study of the stability of Halanay inequalities and enriches the application area of the fixed point method.