We introduce a new iterative scheme for finding a common fixed point of three Suzuki's generalized nonexpansive mappings in Banach spaces. We establish weak and strong convergence theorems for three Suzuki's generalized nonexpansive mappings. The results obtained extend and improve the recent ones announced by Ali et al. \cite{AAKumar}, Maniu \cite{Maniu} and Thakur et al. \cite{Thakur}.