– In This Paper, We Introduced Theconcept of Quasi B-Normal Spaces In Topological Spaces By Using B-Open Sets Dueto Andrijevic [1] and Obtained Several Properties of Such Space. We Introducedthe Concepts of Gb-Closed, Pgb-Closed, Almostb-Closed, Almost Gb-Closed, Almost Pgb- Closed, Pgb-Continuous and Almost Pgb-Continuous Functions. Moreover, We Obtain some Newcharacterizations and Preservation Theorems of Quasi B-Normal Spaces.