Memristors have been widely studied as artificial synapses in neuromorphic circuits, due to their functional similarity with biological synapses, low operating power, and high integration density. Currently, the synaptic weight symbolic limitation and weight update inaccuracy are two challenging issues to be solved. In this work, a novel memristive synapse and a matched mixed-signal neuron circuit are designed to implement robust yet accurate spike-timing-dependent plasticity learning in excitatory and inhibitory synapses. To break through the weight symbolic limitation, a four memristors and two resistors (4M2R) synapse composed of 4M2R for spiking neural network (SNN) is designed. The proposed synapse can be either excitatory or inhibitory (E/I) by rationally arranging the resistors in the circuit, and it is the first of its kind, enabling Hebbian and anti-Hebbian training without additional adjusting of neural signals. In addition, the high symmetricity, linearity, and stability against device variation of the 4M2R synapse can also greatly improve the weight update accuracy. To further address the inaccurate weight update issue caused by signal complexity, a neuron circuit is designed to generate square-wave pulses for spike transmission and synaptic weight modulation. Simulations are carried out in the MATLAB Simscape as well as Virtuoso using SMIC 0.18 <inline-formula> <tex-math notation="LaTeX">\mu </tex-math> </inline-formula>m process and a specially developed memristor model for SNN synapse simulation. The simulating results show good agreement with the weight change derived from the algorithmic methods, and the influence of weak signal-induced weight variation on circuit performance can be rigorously assessed.