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In this paper we introduce Bδg separation axioms and study their basic properties.
We also studied the relations between these axioms and Bδg closed sets and Bδg open sets We give necessary and sufficient condition for a singleton sub set of closed set to be Bδg-T_0 space. Also we have given the equivalent condition for a space X to be a Bδg-T_1 space. A space X is Bδg-T_2 space if and only if for each pair of distinct points x,y∈X, there exists a Bδg-clopen set containing one of them but not the other.