Summary: Using the idea of Halpern’s iteration, we prove a strong convergence theorem for two generalized nonexpansive mappings in a Banach space. It seems that such a strong convergence theorem for generalized nonexpansive mappings is first under Halpern’s iteration process in a Banach space. We apply this result to get well-known and new strong convergence theorems which are connected with generalized nonexpansive mappings in Hilbert spaces and in Banach spaces.