Single Carrier Frequency Division Multiple Access (SC-FDMA) scheme has been considered to be promising technology for the uplink of the 4G mobile communication systems. In spite of the precoding application, SC-FDMA signal using the standard M-QAM base-band modulation scheme still suffers from its high envelope fluctuation resulting in a nonlinear distortion of the transmitted signals due to the transmitter High Power Amplifier (HPA). In order to improve the SC-FDMA performance, the M-ary Amplitude Phase Shift Keying (M-APSK) is proposed as a base-band modulation scheme for SC-FDMA in this study. The application of M-APSK for SC-FDMA has been motivated by its high spectrum efficiency and at the same, time smaller signal fluctuation of the M-APSK signals than that of M-QAM. The performance properties of M-APSK and M-QAM based SC-FDMA transmission scheme will be illustrated using numerical results. The obtained results will show very clearly that the M-APSK based SC-FDMA transmission can provide the preferable performance to M-QAM SC-FDMA if the nonlinear operation of HPA has to be assumed.