A trunnion suspension structure comprising a cross member bridging over a frame constituted by channel steels spaced apart laterally of a vehicle such that channels of said channel steels face with each other, trunnion brackets mounted on lower surfaces of opposite ends of said cross member laterally of the vehicle through fastening members, respectively, a trunnion shaft arranged to bridge over boss parts of said trunnion brackets and having opposite ends respectively projecting outward from said boss parts, central portions of leaf springs being pivotably mounted on said opposite ends of the trunnion shaft through pivotal bases, respectively, each of said trunnion brackets being integrally formed with a trunnion plate part extending upward from an outer surface of said trunnion bracket and mounted on an outer surface of a web of said frame through fastening members, a first closed cross-section structure being provided longitudinally of the cross member and laterally of the vehicle by said cross member, the frame, the trunnion plate parts, the trunnion brackets and the trunnion shaft, a second closed cross-section structure being provided at each of the opposite ends of said cross member laterally of the vehicle by the end of said cross member, the frame, the trunnion plate part and the trunnion bracket, characterized in that upper surfaces of said trunnion brackets facing the lower surfaces of the opposite ends of said cross member laterally of the vehicle being respectively formed with curved concave surface parts curved downward and extending into said trunnion plate parts, a third closed cross-section structures being provided, at each of the opposite ends of said cross member laterally of the vehicle, by the end of said cross member, the frame, the curved concave surface part of said trunnion bracket and the trunnion plate part. a cross member bridging over a frame constituted by channel steels spaced apart laterally of a vehicle such that channels of said channel steels face with each other, trunnion brackets mounted on lower surfaces of opposite ends of said cross member laterally of the vehicle through fastening members, respectively, a trunnion shaft arranged to bridge over boss parts of said trunnion brackets and having opposite ends respectively projecting outward from said boss parts, central portions of leaf springs being pivotably mounted on said opposite ends of the trunnion shaft through pivotal bases, respectively, each of said trunnion brackets being integrally formed with a trunnion plate part extending upward from an outer surface of said trunnion bracket and mounted on an outer surface of a web of said frame through fastening members, trunnion brackets mounted on lower surfaces of opposite ends of said cross member laterally of the vehicle through fastening members, respectively, a trunnion shaft arranged to bridge over boss parts of said trunnion brackets and having opposite ends respectively projecting outward from said boss parts, central portions of leaf springs being pivotably mounted on said opposite ends of the trunnion shaft through pivotal bases, respectively, each of said trunnion brackets being integrally formed with a trunnion plate part extending upward from an outer surface of said trunnion bracket and mounted on an outer surface of a web of said frame through fastening members, a first closed cross-section structure being provided longitudinally of the cross member and laterally of the vehicle by said cross member, the frame, the trunnion plate parts, the trunnion brackets and the trunnion shaft, a second closed cross-section structure being provided at each of the opposite ends of said cross member laterally of the vehicle by the end of said cross member, the frame, the trunnion plate part and the trunnion bracket, characterized in that upper surfaces of said trunnion brackets facing the lower surfaces of the opposite ends of said cross member laterally of the vehicle being respectively formed with curved concave surface parts curved downward and extending into said trunnion plate parts, a third closed cross-section structures being provided, at each of the opposite ends of said cross member laterally of the vehicle, by the end of said cross member, the frame, the curved concave surface part of said trunnion bracket and the trunnion plate part. a third closed cross-section structures being provided, at each of the opposite ends of said cross member laterally of the vehicle, by the end of said cross member, the frame, the curved concave surface part of said trunnion bracket and the trunnion plate part.