Let C be a closed convex subset of a real Hilbert space H and assume that T is an asymptotically κ-strict pseudo-contraction on C with a fixed point, for some 0≤κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0, 1), the modified Mann’s algorithm generates a sequence {xn} via the formula: xn+1=αnxn+(1−αn)Tnxn, n≥0. It is proved that if the control sequence {αn} is chosen so that κ+δ<αn<1−δ for some δ∈(0,1), then {xn} converges weakly to a fixed point of T. We also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence.