The frequency diverse multiple-input multiple-output (FD-MIMO) sonar can achieve improved detection performance in the range dimension by synthesizing echoes at different frequency bands without over-demanding system bandwidth. However, the existing bandwidth synthesis (BS) method suffers from high-level range sidelobes caused by the spectral leakage of the subband signals and the discontinuity of the synthesized spectrum. Hence, it is hard to detect a weak target in the range dimension. To address this problem, a deconvolved bandwidth synthesis (DBS) method is proposed, which can suppress the range-dimensional sidelobes by post-processing the beam output of the synthesized spectrum. To be specific, we first employ the narrowband frequency diverse linear frequency modulated (FD-LFM) pulses to construct the range-dimensional point spread function (PSF), and then apply the PSF and the Richardson-Lucy (R-L) algorithm to deconvolve the data obtained by synthesizing spectra of the subband signals. Simulation results indicate that for the FD-MIMO sonar the proposed DBS method shows a better interference rejection ability and a higher range resolution in the range dimension than the BS method.