A novel microfluidic flowmeter integrated with microfiber Bragg grating (µFBG) is presented. Two glass capillaries and a short length of high-light-absorption Co²⁺-doped optical fiber were stacked inside a larger outer capillary tube. The stack was then drawn into a tapered device. Two microchannels with the diameter of ~50 μm were formed inside the capillaries for flowing of microfluidics. An FBG was inscribed in the tapered Co²⁺-doped fiber with waist diameter of ~70 μm, and acts as a flow-rate sensor. A pump laser with wavelength of 1480 nm was utilized to locally heat the µFBG, rendering the µFBG as miniature "hot-wire" flowmeter. The flow rate of the liquid in the microchannels is determined by the induced wavelength shift of the µFBG. The experimental results achieve a minimum detectable change of ~16 nL/s in flow rate, which is very promising in the use as part of biochips.