Short-offset towed streamer data, and sparse ocean-bottom seismometer (OBS) data are not conducive to applying multi-parameter full waveform inversion (FWI) in production. It is challenging to reconstruct deep velocity in the former, and the latter suffers from severe acquisition footprints. We developed a joint acoustic-elastic coupled full waveform inversion (J-AEFWI) method, in which towed streamer data and ocean-bottom seismometer data were used jointly to build P-wave and S-wave velocity models. A new joint objective function was established using the least-squares theory, and the joint acoustic-elastic coupled full waveform inversion method on the acoustic-elastic coupled equation was derived. The method can inject the residuals of the towed streamer data and the ocean-bottom seismometer data in time backward propagating to update P-wave and S-wave velocity models. The synthetic experimental results show that joint acoustic-elastic coupled full waveform inversion obtains more accurate results than when using these two types of data alone. Compared to using the towed streamer or ocean-bottom seismometer data alone, the joint acoustic-elastic coupled full waveform inversion method leads to better illumination of the deep background velocities and suppression of acquisition footprints. The results of joint acoustic-elastic coupled full waveform inversion were slightly better than those of the cascaded full waveform inversion strategy. To further demonstrate the benefit of the proposed method, we applied it to the field data, and better results are obtained as expected.