We describe a control algorithm that can improve accuracy and stability of flow regulation in a microfluidic network that uses a conventional pressure pump system. The algorithm enables simultaneous and independent control of fluid flows in multiple micro-channels of a microfluidic network, but does not require any model parameters or tuning process. We investigate robustness and optimality of the proposed control algorithm and those are verified by simulations and experiments. In addition, the control algorithm is compared with a conventional PID controller to show that the proposed control algorithm resolves critical problems induced by the PID control. The capability of the control algorithm can be used not only in high-precision flow regulation in the presence of disturbance, but in some useful functions for lab-on-a-chip devices such as regulation of volumetric flow rate, interface position control of two laminar flows, valveless flow switching, droplet generation and particle manipulation. We demonstrate those functions and also suggest further potential biological applications which can be accomplished by the proposed control framework.