Optical isolators are indispensable components of almost any optical system and are used to protect a laser from unwanted reflections for phase-stable coherent operation. The emergence of chip-scale optical systems, powered by semiconductor lasers that are integrated on the same chip, has generated a demand for a fully integrated optical isolator. Conventional approaches, which rely on the use of magneto-optic materials to break Lorentz reciprocity, present substantial challenges in terms of material integration. Although alternative magnetic-free approaches have been explored, an integrated isolator with a low insertion loss, high isolation ratio, broad bandwidth and low power consumption on a monolithic material platform is yet to be achieved. Here we realize a non-reciprocal travelling-wave-based electro-optic isolator on thin-film lithium niobate. The isolator enables a maximum optical isolation of 48.0 dB with an on-chip insertion loss of 0.5 dB and uses a single-frequency microwave drive power of 21 dBm. The isolation ratio remains larger than 37 dB across a tunable optical wavelength range from 1,510 to 1,630 nm. We realize a hybrid distributed feedback laser–lithium niobate isolator module that successfully protects the single-mode operation and linewidth of the laser from reflection. Our result represents an important step towards a practical high-performance optical isolator on chip. An integrated electro-optic isolator on thin-film lithium niobate enables non-reciprocal isolation by microwave-driven travelling-wave phase modulation. The isolator exhibits a maximum optical isolation of 48.0 dB at around 1,553 nm and an on-chip insertion loss of 0.5 dB.