A pipe line for fluid to be detected is formed so that heat from a flow rate detector in which a thin-film heating element and a thin-film temperature sensing element are laminated on a first surface of a substrate through an insulating layer is transferred to and absorbed by the fluid. In the flow rate detector, the temperature sensing which is affected by the heat absorption of the fluid due to the heating of the thin-film heating element is executed by the thin-film temperature sensing element, and the flow rate of the fluid in the pipe line is detected on the basis of the temperature sensing result. A fin plate extending into the pipe line is joined to a second surface of the substrate of the flow rate detector by a joint member, and the fin plate extends so as to pass through the central portion on the circular section of the pipe line. The dimension of the fin plate in the direction of the pipe line is larger than the dimension L2 of the thickness. Accordingly, even when the fluid is viscous fluid having relatively high viscosity, and further even when the flow rate is relatively small or under a broad environmental temperature condition, the flow rate of the fluid-flowing in the pipe line can be accurately measured.