The integrated Synthetic Aperture Radar (SAR) and Communication system can improve the networking capabilities of SAR, realize the real-time transmission of detection data, and improve the overall performance of the system. In the working process of the integrated platform, Doppler shift and multipath effects will be introduced, which make the orthogonality of the widely studied Orthogonal Frequency Division Multiplexing (OFDM) integrated waveforms unable to be maintained, and the imaging and communication performance is impaired. In this paper, the Filter Bank Multicarrier (FBMC) waveform used for the integrated SAR and communication systems is proposed. On the one hand, FBMC waveforms require low orthogonality between subcarriers, which can counter Doppler and multipath effects. On the other hand, FBMC waveforms do not use Cyclic Prefix (CP), so the false targets can be avoided and spectral efficiency can be improved. This paper analyzes the integrated performance of FBMC waveforms, studies the effects of multipath and Doppler shift on FBMC waveforms in the integrated system, and proposes a Doppler compensation algorithm for integrated FBMC waveform with large frequency shift. According to the above analysis, the FBMC waveform has better performance in the wide swath SAR and communication integration system. Simulation results verify the conclusion.