A print head is disclosed for use with an additive manufacturing system. The print head may include a housing configured to receive a prefabricated woven sleeve, and a fiber guide disposed at least partially inside the housing and configured for insertion into the prefabricated woven sleeve. The print head may also include a diverter connected to an end of the fiber guide inside of a downstream mouth of the housing, and at least one cure enhancer located at the mouth of the housing.