We present a revolutionary on-chip pumping with high-speed response, high-resolution and bidirectional continuous pumping. Generally, there is a tough challenge of on-chip pumping to break through the trade-off between response time and volumetric resolution with the function of bidirectional continuous pumping. In order to confront this challenge, we propose a concept of 'asymmetric flow resistors (AFRs)' whose flow resistance is temporally changed by utilizing the spatiotemporal vortices generated by physical interaction between ultrafast flow and uniquely designed asymmetric microstructures of microchannel. Thus, we achieved an unexplored specification of on-chip pumping with resolution of 1.4 nl with the single forward-backward actuation and response time of <50 ms with continuous flow. Furthermore, we demonstrated bidirectional pumping of picking-up and dispensing of single motile microalga by using a microfluidic pipette utilizing two proposed on-chip pumps with opposite direction.