Optical memristors represent a monumental leap in the fusion of photonics and electronics for neuromorphic computing and artificial intelligence. Here, we reveal the first lead zirconate titanate (PZT) optical memristor, working with a paradigm of functional duality: non-volatile setting and ultrafast volatile modulation via the Pockels effect. Fine-tuning and large modulation depth are achieved with an index change of 4.6 × 10-3 when setting above a threshold voltage Vth and the switching energy is 12.3 pJ only. The non-volatility is highly stable even with >100,000 cycles. Sub-nanosecond volatile modulation (48 Gbps, 432 fJ/bit) is realized with high efficiency (VπL ~ 0.5 V·cm) via the strong Pockels effect below Vth. Our wafer-scale manufacturing process shows great potential for mass production. The present PZT optical memristors bridge the gap between high-speed photonics and non-volatile memory, offering transformative potential for high-speed and energy-efficient optical interconnects, quantum computing, neural networks, in-memory computing, and brain-like architecture.