The purpose of this article is to introduce some results on fuzzy supra Baire spaces and other fuzzy supra topological spaces. The characterization and relation between fuzzy supra strongly hyperconnected spaces and fuzzy supra Baire spaces were carried out. From the results, we have shown that fuzzy supra strongly hyperconnected spaces which are not fuzzy supra Baire spaces. In addition, fuzzy supra strongly hyperconnected spaces are fuzzy supra nodec space, fuzzy supra hyperconnected space and fuzzy supra open hereditarily irresolvable space were discussed.