In this paper, we introduce a new class of Bi-topological space called Bi*-topological space. Also, introduce and study Bi*-topological properties of bi∗-open (bi∗∗-open) sets and bi∗-closed (bi∗∗-closed) sets, etc. Moreover, introduce and study some type of sets in Bi∗-topological space and also some type of continuous functions in Bi∗-topological space