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This contribution applies digital predistorter to compensate distortions caused by memory high power amplifiers (HPAs) which exhibit true output saturation characteristics. Particle swarm optimization is first implemented to identify the Wiener HPA's parameters. The estimated Wiener HPA model is then directly used to design the predistorter. The proposed digital predistorter solution is attractive owing to its low on-line computational complexity, small memory units required and simple VLSI hardware structure implementation. Moreover, the designed predistorter is capable of successfully compensating serious nonlinear distortions and memory effects caused by the memory HPA operating in the output saturation region. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.