A flow-rate measurement apparatus comprising: a main passage; a sub-passage configured to take part of a fluid flowing through the main passage; and a plate-shaped board having a sensor element for measuring a mass flow of the fluid, which is mounted on a sensor-element mounting surface side thereof, wherein the plate-shaped board is arranged in a second sub-passage portion of the sub-passage so that fluid passages are respectively formed at the sensor-element mounting surface side and a backside surface side of the plate-shaped board, the backside surface side being the opposite side of the plate-shaped board to the sensor-element mounting surface side, the sensor-element mounting surface side and the backside surface side of the plate-shaped board are disposed being parallel to the direction of fluid flowing in the second sub-passage portion, the sub-passage includes a curved first sub-passage portion which is located upstream of the plate-shaped board and which changes its direction so as to form a curved flow passage portion, whereby the sub-passage has a first sidewall surface and a second sidewall surface opposed to the first sidewall surface, the first sidewall surface facing the sensor-element mounting surface, the second sidewall surface facing the backside surface, the curved first sub-passage portion further has an outer-circumferential wall surface (10G, 10H) and an inner-side wall surface, and the outer-circumferential wall surface (10G, 10H) includes a sloping portion that slopes towards the inner side-wall surface so that, of two edge portions of the outer-circumferential wall surface (10G, 10H) in a direction perpendicular to the sensor-element mounting and backside surfaces (5a, 5b) of the plate-shaped board, the edge portion located on the first sidewall surface of the curved first sub-passage portion is positioned closer to the inner wall surface of the curved first sub-passage portion than the edge portion on the second sidewall surface of the curved first sub-passage portion. a main passage; a sub-passage configured to take part of a fluid flowing through the main passage; and a plate-shaped board having a sensor element for measuring a mass flow of the fluid, which is mounted on a sensor-element mounting surface side thereof, wherein the plate-shaped board is arranged in a second sub-passage portion of the sub-passage so that fluid passages are respectively formed at the sensor-element mounting surface side and a backside surface side of the plate-shaped board, the backside surface side being the opposite side of the plate-shaped board to the sensor-element mounting surface side, the sensor-element mounting surface side and the backside surface side of the plate-shaped board are disposed being parallel to the direction of fluid flowing in the second sub-passage portion, the sub-passage includes a curved first sub-passage portion which is located upstream of the plate-shaped board and which changes its direction so as to form a curved flow passage portion, whereby the sub-passage has a first sidewall surface and a second sidewall surface opposed to the first sidewall surface, the first sidewall surface facing the sensor-element mounting surface, the second sidewall surface facing the backside surface, the curved first sub-passage portion further has an outer-circumferential wall surface (10G, 10H) and an inner-side wall surface, and the outer-circumferential wall surface (10G, 10H) includes a sloping portion that slopes towards the inner side-wall surface so that, of two edge portions of the outer-circumferential wall surface (10G, 10H) in a direction perpendicular to the sensor-element mounting and backside surfaces (5a, 5b) of the plate-shaped board, the edge portion located on the first sidewall surface of the curved first sub-passage portion is positioned closer to the inner wall surface of the curved first sub-passage portion than the edge portion on the second sidewall surface of the curved first sub-passage portion.