A winding section of a filament winding apparatus winds a fiber bundle around a filament-wound member. A tension acquisition part acquires a detected winding-tension value. A supply-speed acquisition part acquires a detected supply-speed value. A storage part stores correlation information in which an allowable determination range of winding tension is set in relation to the supply speed. A determination part determines whether the winding of the fiber bundle is successful or unsuccessful by comparing detected-value information, including the detected winding-tension value and the detected supply-speed value associated with each other, with the correlation information.