The aim of this paper is to study some main properties of convex fuzzy cones of hypervector spaces. In this regard, a characterization of fuzzy subhyperspaces is presented based on ordinary subhyperspaces. Also the convex cone spanned by non-empty subsets of real hypervector spaces is obtained. Moreover, by introducing the notion of fuzzy cone, the smallest fuzzy subhyperspace of V containing µ and the largest fuzzy subhyperspace of V contained in µ is achieved, for a convex fuzzy cone µ of real hypervector space V .