Abstract: In an infinite dimensional Hilbert space, the normal Mann's iterative algorithm has only weak convergence, in general, even for non-expansive mappings. In order to get a strong convergence result, the normal Mann's iterative algorithm is modified by using a suitable convex combination of a fixed vector and a sequence in a closed convex subset of a real Hilbert space. A strong convergence theorem is established by means of a new Ishikawa-like iterative algorithm for κ-strict pseudo-contractions in Hilbert spaces. The results presented in this paper have extended and improved some recent results.