Abstract: Let a,b be two generalized Drazin invertible elements in a Banach algebra, a^d be the generalized Drazin inverse of aaⁿd a^π=1-aa^d. We  gave the expressions for the generalized Drazin [JP2]inverse of the sum a+b  under some conditions such as ab^π=a, b^πba^π=b^πb, b^πa^πa²b=b^πa^πaba, b^πa^πb²a=b^πa^πbab etc by using the idempotent element in a Banach algebra.

Key words: generalized Drazin inverse, Banach algebra, quasinilpotent element