Abstract: The definition of global polynomial stability for a class of impulsive recurrent neural networks (IRNNs) with proportional delays is given. By introducing adjustable parameters, several suitable Lyapunov functionals are constructed and the method of linear matrix inequality (LMI) is used to discuss the global polynomial stability of the system. Several criteria for guaranteeing the global polynomial stability of the system are obtained. And these criteria are given in the form of LMI, which is convenient to use Matlab toolbox for verification. The relationship between polynomial stability and exponential stability is revealed. The criteria are verified by numerical examples.