Summary: A strong convergence theorem of an averaging composite implicit iteration process to the common fixed points of a finite family of asymptotically pseudo-contractive mappings is proved in Banach spaces. Our results generalize and complement the results of Y.-F. Su and S.-H. Li [J. Math. Anal. Appl. 320, No. 2, 882–891 (2006; Zbl 1095.47045)], and M. O. Osilike and B. G. Akuchu [Fixed Point Theory Appl. 2004, No. 2, 81–88 (2004; Zbl 1088.47510)].