A device for measuring the flow of a fluid in a fluid channel, with at least one thermocouple, whose thermojunctions are arranged one behind the other in the direction of flow of the fluid and are maintained at a working temperature higher than the fluid temperature by means of an ac power source 9. The thermocouple is connected to a measuring circuit evaluating the thermocouple voltage U.sub.T. Continuous measurement with high accuracy is possible with a measuring circuit having a switching network, by which the ac power source is connected to the thermocouple at least during the measurement phase, and by which the ac voltage components superimposed to the thermocouple voltage are eliminated by subtraction.