We present an antibody-free approach for the high-purity and high-throughput dielectrophoretic (DEP) isolation of circulating tumour cells (CTCs) from blood in a microfluidic chip. A hydrodynamic sheath flow is designed upstream in the chip to direct the suspension samples to the channel side walls, thus providing a queue to allow DEP-induced lateral displacements. High-throughput continuous cancer cell sorting (maximum flow rate: ~2.4 mL h(-1), linear velocity: ~4 mm s(-1)) is achieved with a sustained 3D lateral DEP (LDEP) particle force normal to the continuous through-flow. This design allows the continuous fractionation of micro/nanosized particles into different downstream subchannels based on the differences in their different critical negative DEP strengths/mobilities. The main advantage of this separation strategy is that increasing the channel length can effectively increase the throughput proportionally. The effective separation of rare cancer cells (<0.001%) from diluted human blood in a handheld chip is demonstrated. An enrichment factor of 10(5) and a recovery rate of ~85% from a 0.001% cancer cell sample are achieved at an optimal flow rate of 20 μL min(-1) passing through a 6 cm long LDEP channel with an appropriate voltage at a frequency of 10 kHz. A higher throughput of 2.4 mL h(-1) is also achieved with a 13 cm long metal-based microchannel.