This paper presents a new adaptive pre-distortion (PD) technique, based on neural networks (NN) with tap delay line for linearization of High Power Amplifier (HPA) exhibiting memory effects. The adaptation, based on iterative algorithm, is derived from direct learning for the NN PD. Equally important, the paper puts forward the studies concerning the application of different NN learning algorithms in order to determine the most adequate for this NN PD. This comparison examined through computer simulation for 64 carriers and 16-QAM OFDM system, is based on some quality measure (Mean Square Error), the required training time to reach a particular quality level and computation complexity. The chosen adaptive pre-distortion (NN structure associated with an adaptive algorithm) have a low complexity, fast convergence and best performance.