Recently, dynamic power supply voltage techniques, such as an Envelope Elimination and Restoration power amplifier (EER-PA) or Envelope-Tracking Power amplifier (ET-PA), have been attracting much attention because they can maintain high efficiency in large back-off region [1]-[6]. The dynamic power supply voltage techniques cause strong nonlinearity compared to a conventional power amplifier, hence a memoryless Digital Predistortion (DPD) technique is indispensable for these efficiency enhancement techniques. However, the performance of the memoryless DPD is degraded due to the frequency response of the envelope amplifier in the dynamic power supply voltage techniques [7]-[9]. In this paper, we clarify the degradation mechanisms of the memoryless DPD for the EER-PA due to the frequency response of the envelope amplifier based on the results of two-tone tests, and propose an analytical model for improving the performance of the memoryless DPD developed for the EER-PA. In addition, a prototype EER-PA is developed and we demonstrate that the residual distortion of the developed EER-PA with conventional memoryless DPD algorithm is compensated by the new algorithm based on the proposed analytical model. In the two-tone test, third-order intermodulation distortion (IMD3) with a tone spacing from 100 kHz to 4 MHz is improvement by up to 25 dB by the memoryless DPD algorithm based on the proposed model. Measured adjacent channel leakage power ratio (ACPR) of the developed EER-PA is improved from -22.5 dBc to -42.5 dBc in the OFDM signal test with 1.08 MHz bandwidth.