Abstract: Using the system of idempotents in a Banach algebra, we considered the generalized Drazin inverse of the sum of two elements. For two elements a,b
 in a Banach algebra, we gave the expressions for the generalized Drazin inverse of the sum a+b under the condition that b²a=a^πbabb^π, a²b=a^πabab^π.

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