The main purpose of this paper is to study an iteration procedure for
 finding a common fixed point of a countable family of nonexpansive
 mappings in Banach spaces. We introduce a Mann type iteration
 procedure. Then we prove that such a sequence converges weakly to a
 common fixed point of a countable family of nonexpansive
 mappings. Moreover, we apply our result to the problem of finding a
 common fixed point of a pair of nonexpansive mappings and the problem
 of finding a common solution of the fixed point problem and the
 variational inequality problem.