In this paper, global h-stability of nonlinear positive Cohen-Grossberg neural network (PCGNN) system with time-varying delays is studied by means of a direct analysis method. By selecting the appropriate h function and determining its differential expression, global h-stability is converted into two types of known stability, that is Lagrangian exponential stability and global exponential stability. For the sake of improving the accuracy of the stability results, we spare no effort to optimize the fitting effect of the system state trajectory by changing the differential expression of the h function. In addition, two examples are given to verify the feasibility and effectiveness of this method in PCGNN.