The memristor, a promising candidate for synaptic interconnections in artificial neural network, has gained significant attention for application to neuromorphic systems. One common method is using two memristors as one synapse to represent the positive and negative weights. In this paper, the synaptic behavior of a Ag/AgInSbTe/Ta (AIST)-based memristor is experimentally demonstrated. In addition, a neural architecture using one AIST memristor as a synapse is proposed, where both the plus and minus weights of the neural synapses are realized in a single memristive array. Moreover, the memristor-based neural network is extended to a multilayer architecture, and modified memristor-based backpropagation learning rules are implemented on-chip to achieve pattern recognition. The effects of device variations and input noise on the performance of a memristor-based multilayer neural network (MNN) are also described. The proposed MNN is capable of pattern recognition with high success rates and exhibits several advantages, such as good accuracy, high robustness, and noise immunity.