The memristor-based neural network configuration is a promising approach to realizing artificial neural networks (ANNs) at the hardware level. The memristors can effectively simulate the strength of synaptic connections between neurons in neural networks due to their diverse significant characteristics such as nonvolatility, nanoscale dimensions, and variable conductance. This work presents a new synaptic circuit based on memristors and Complementary Metal Oxide Semiconductor(CMOS), which can realize the adjustment of positive, negative, and zero synaptic weights using only one control signal. The relationship between synaptic weights and the duration of control signals is also explained in detail. Accordingly, Widrow–Hoff algorithm-based memristive neural network (MNN) circuits are proposed to solve the recognition of three types of character pictures. The functionality of the proposed configurations is verified using SPICE simulation.