Chidume first introduced the definition of asymptotically nonexpansive nonself-mappings and uniformly L-Lipschitzan nonself mappings. Furthermore he proved that the iterative sequence converged strongly to fixed points of asymototically nonexpansive nonselfmappings . In this paper, the definition of asymptotically pseudo-contractive type nonself-mappings, asymptotically quasi pseudo-contractive type nonself-mappings is introduced. Suppose E is a real Banach space, let K be a retract of E, P be a nonexpansive retraction from E to K ,T is L-Lipschitzan asymptotically quasi pseudo-contractive type nonself-mappings , under some restricted conditions on the parameters. An necessary and sufficient condition is given for the modified Ishikawa iterative sequence with error to converge strongly to a fixed point of T, Suppose there exist a strictly increasing function*, such that lim sup inf *. The objective of this article is to extend the asymptotically quasi pseudo-contractive type mappings to asymptotically quasi pseudo-contractive type nonself-mappings. Therefore, the results presented in this paper extended the previous work.(* Indicates a formula, please see the full text)