In this paper, some additive properties of the pseudo Drazin inverse are obtained in a Banach algebra. In addition, we find some new conditions under which the pseudo Drazin inverse of the sum $a+b$ can be explicitly expressed in terms of $a,a^\ddag,b,b^\ddag$. In particular, necessary and sufficient conditions for the existence as well as the expression for the pseudo Drazin inverse of the sum $a+b$ are obtained under certain conditions. Also, a result of Wang and Chen [Pseudo Drazin inverses in associative rings and Banach algebras, LAA 437(2012) 1332-1345] is extended.