In order to develop all-optical flowrate measurement technology, a hot-wire flowmeter based on cobalt-doped high-attenuation fiber Bragg grating is proposed, and the flowrate measurement is achieved by demodulating the central wavelength of the fiber Bragg grating. The research process includes sensor fabrication, temperature sensing characteristics measurement and flowrate measurement experiments. The results show that the fiber Bragg grating has a temperature sensitivity of 10.3 pm/°C based on the fiber with an attenuation coefficient of 8.9 dB/cm (1480 nm), and the flowmeter can realize highly repeatable measurements in the range of 400~3700 L/h. The flowrate and the central wavelength of the fiber Bragg grating follow a specific nonlinear function. The average sensitivity of the flowmeter is about 0.15 pm/(L·h^-1), and the sensitivity can be up to 1 pm/(L·h^-1) at lower flow rates. The proposed flowmeter enriches the research of fiber Bragg grating for liquid flow measurement. In the design, cobalt-doped high attenuation fiber self-heating and single-end capillary packaging are used, which provides a new idea for the development of full optics, miniaturization and high sensitivity of flow sensor.