A combined digital pre-distortion (DPD) and peak to average power ratio (PAPR) reduction for Filtered Orthogonal Frequency Division Multiplexing (F-OFDM) systems is proposed where F-OFDM is one of the candidates for 5G waveform technology. In the system, the power amplifier (PA) will produce nonlinear distortion because it works in the saturation region and the high PAPR. DPD based on PAPR reduction structure may be adopted to compensate the nonlinear resulting from PAs. Firstly, in order to reduce the PAPR, a low complexity iterative partial transmission sequence (IPTS) algorithm combined with iterative clipping revision (ICR) is introduced. And then, the joint structure of DPD and IPTS-ICR is proposed. Simulation results show that the proposed structure can improve the PAPR suppression performance of F-OFDM system compared to low complexity IPTS algorithm or ICR algorithm alone. The proposed structure can also effectively improve the nonlinear distortion of the F-OFDM system.