This paper describes a method to design a predistorter (PD) for a GaN-FET power amplifier (PA) by using nonlinear parameters extracted from measured IMD which has asymmetrical peaks peculiar to a memory effect with a second-order lag. While, computationally efficient equations have been reported by C. Rey et al. for the memory effect with a first-order lag. Their equations are extended to be applicable to the memory effect with the second-order lag. The extension provides a recursive algorithm for cancellation signals of the PD each of which updating is made by using signals in only two sampling points. The algorithm is equivalent to a memory depth of two in computational efficiency. The required times for multiplications and additions are counted for the updating of all the cancellation signals and it is confirmed that the algorithm reduces computational intensity lower than half of a memory polynomial in recent papers. A computer simulation has clarified that the PD improves the adjacent channel leakage power ratio (ACLR) of OFDM signals with several hundred subcarriers corresponding to 4G mobile radio communications. It has been confirmed that a fifth-order PD is effective up to a higher power level close to 1dB compression. The improvement of error vector magnitude (EVM) by the PD is also simulated for OFDM signals of which the subcarrier channels are modulated by 16 QAM.