Abstract: This paper investigates the global asymptotic stability of the neural networks with discrete and infinite distributed delays. Without assuming the boundedness and differentiability of neuron activation function, a new criteria is proposed by way of constructing a suitable Lyapunov function. Using Hadamard product, a vector-matrix form of neural networks with infinite distributed delays is obtained. It solves the problem with infinite distributed delays only by imposing constraints on the interconnected matrices and derivative of time delays. The condition is expressed by a linear matrix inequality, which can be easily computed in MATLAB toolbox. Comparisons between the results and the existing ones through two numerical examples imply the effectiveness of the proposed result.