Two-dimensional boron (borophene) is featured by its structural polymorphs and distinct in-plane anisotropy, opening opportunities to achieve tailored electronic properties by intermixing different phases. Here, using scanning tunneling spectroscopy combined with first-principles calculations, delocalized one-dimensional nearly free electron states (NFE) in the (2,3) or b{eta}12 borophene sheet on the Ag(111) surface were observed. The NFE states emerge from a line defect in the borophene, manifested as a structural unit of the (2,2) or c{hi}3 sheet, which creates an in-plane potential well that shifts the states toward the Fermi level. The NFE states are held in the 2D plane of borophene, rather than in the vacuum region as observed in other nanostructures. Furthermore the borophene can provide a rare prototype to further study novel NFE behaviors, which may have potential applications on transport or field emission nanodevices based on boron.