We investigate the global exponential stability of CohenGrossberg neural networks (CGNNs) with variable moments of impulses using B-equivalence method. Under certain conditions, we show that each solution of the considered system intersects each surface of discontinuity exactly once, and that the variable-time impulsive systems can be reduced to the fixed-time impulsive ones. The obtained results imply that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing, and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points. Moreover, two stability criteria for the considered CGNN by use of proposed comparison system are obtained. Finally, the theoretical results are illustrated by two examples.