The oversampled OFDM modulation is a possible alternative to conventional OFDM for the transmission of signals over multipath fading channels. Indeed with oversampled OFDM, appropriate pulse-shaping can be introduced to fight against time and frequency dispersion. In this paper, we propose a theoretical and experimental analysis of the peak-to-average power ratio (PAPR) of oversampled OFDM. Our analysis illustrates the impact of the oversampling ratio and of the pulse shape on the PAPR distribution