Several LUT-based pre-distortion schemes using Saleh's model for compensation of RF non-linearity have been studied recently. In this paper we propose a novel parameter-based predistorter to enhance the power efficiency of mobile OFDM transmitters using solid-state power amplifiers (SSPA). Both the non-linearity and inverse of the non-linearity are estimated as memory-less polynomials using least squares (LS) criterion. A fully digital pre-distorter is then constructed with a closed-form inverse non-linearity to reduce the in-band non-linear distortion and out-of-band spectrum re-growth in the transmitter. Simulation results in 16-QAM OFDM show promising performance and simple implementation compared with the LUT method.