Abstract: To address the problem of reconstructing multiband signals with unknown support set， this paper proposed a blind multiband signal predistortion model based on compressive sampling structure， the multiband output signal was considered as a single broadband signal， and after down conversion and low pass filter processing， it was fed into the alternate modulated wideband converter （A-MWC） structure for blind compressive sampling， the signal was then blindly reconstructed by the variable step sparsity adaptive matching pursuit algorithm based on stochastic support selection （Sto-VSSAMP）. The model reduced the feedback loop bandwidth， decreased the signal sampling rate， and improved the linearization effect of the reconstruction. In this paper， experimental tests are conducted using dual-band signals， the results show that this method improves the reconstructed signal accuracy while the adjacent channel power radio of the power amplifier output signal is improved by about 21 dBc compared with that without predistortion， the normalized mean squared error is improved by about 10 dBc compared with that of the conventional two dimensional digital predistortion （2D-DPD）， and good linearization performance is obtained.