Memristor is considered as a promising synaptic device for neural networks because of its tunable and non-volatile resistance states, which is similar to the biological synapses. In this article, a novel network circuit based on memristor synapses is proposed for bidirectional associative memory with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-situ</i> learning method. An analog neuron circuit is designed to emulate the cubic activation function of neural networks. A memristive synapse circuit is constructed to map both positive and negative weights on a single memristor. Moreover, an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-situ</i> learning circuit fitting memristor's nonlinear characteristic is proposed. Feedback control strategy is incorporated in this learning circuit to adjust the resistance of the memristor and avoid the encoding error of the memristor's write voltage. The performance of the proposed network circuit is verified by the training and recalling simulations. The comparison between the proposed approach and related works is analyzed to demonstrate the advantage of the proposed circuit design.