An apparatus for measuring the flow rate of a gas wherein resistance wires whose resistance value changes in accordance with temperature are arranged in a flow rate measuring tube providing a path of a gas to be measured, a voltage is applied to the resistance wires to detect the change in resistance value of the resistance wires due to the change in temperature thereof in accordance with the gas flow rate, and the flow rate of the gas is measured. In order to support the resistance wires in the flow rate measuring tube, the support members for supporting the resistance wires have respectively two support rods provided with grooves at positions corresponding to the turning points of the resistance wires wound thereon so that the resistance wires are supported stably lying in the grooves.