Brain-inspired neuromorphic computing can overcome the energy and throughput limitations of traditional von Neumann-type computing systems, which requires analog updates of their artificial synaptic strengths for the best recognition performance and low energy consumption. Here, we report synaptic devices made from highly insulating ferroelectric LiNbO₃ (LNO) thin films bonded to SiO₂/Si wafers. Through the creation/annihilation of periodically arrayed antiparallel domains within LNO nanocells, which are stimulated using positive/negative voltage pulses (synaptic plasticity), we can modulate the synaptic conductance linearly by controlling the number of the conducting domain walls. The multilevel conductance is nonvolatile and reproducible with negligible dispersion over 100 switching cycles, representing much better performance than that of random defect-based nonlinear memristors, which generally exhibit large-scale resistance dispersion. The simulation of a neuromorphic network using these LNO artificial synapses achieves 95.6% recognition accuracy for faces, thus approaching the theoretical yield of ideal neuromorphic computing devices.