Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/1478 2022 2022 Department of Mathematics, College of Science, AlFurat University, Deir-ez-Zor, Syria Riad K. Al Al-Hamido In this paper, we introduce infra bi-topological structure which is a more general structure than infra-topological spaces. This new space make us enable to increate a new sub-classes of sets, called  infra bi-open (bi-closed) sets,  pairwise infra-open (closed) sets. also we define infra bi-closure, pairwise infra bi-interior and their basic properties are presented. The relations of these concepts with their counterparts in infra-topological space s are given and many examples are presented. 2023 2023 08 16 10.54216/PAMDA.010201 https://www.americaspg.com/articleinfo/34/show/1478