A simple, low-cost and on-demand microfluidic flow controlling platform was developed based on a unique capillary-tuned solenoid microvalve suction effect without any outer pressure source. The suction effect was innovatively employed as a stable and controllable driving force for the manipulation of the microfluidic system by connecting a piece of capillary between the microvalve and the microfluidic chip, which caused significant hydrodynamic resistance differences among the solenoid valve ports and changed the flowing mode inside the valve. The volume of sucked liquid could be controlled from microliters even down to picoliters either by decreasing the valve energized duration (from a maximum energized duration to the valve response time of 20 ms) or by increasing the inserted capillary length (i.e., its hydrodynamic resistance). Several important microfluidic unit operations such as cell/droplet sorting and on-demand size-controllable droplet generation have been demonstrated on the developed platform and both simulations and experiments confirmed that this platform has good controllability and stability.