The present invention relates to a head for applying fibers in order to make components of composite materials, intended to be mounted at the end of a displacement system for applying to a surface a wide strip formed of a number of fibers. The head comprises an application roller for applying fibers in the form of a strip, means for guiding fibers on said roller, and cutting means including blades activated by activation systems between a rest position and an active cutting position so as to cut the fibers upstream of the application roller. Said blades and associated activation systems are all placed on the side of the roller relative to said fibers.