Multichannel predictive deconvolution can accommodate the lateral variations of subsurface structures to some extent and better preserve primaries than can single-channel predictive deconvolution. To solve the 2D predictive filter, traditional multichannel predictive deconvolution uses the least-squares (LS) algorithm, which requires orthogonality between primaries and multiples. In areas where primaries and multiples overlap, traditional LS-based multichannel predictive deconvolution can cause distorted primaries and residual multiples. To avoid the orthogonality assumption required by the LS algorithm, the iterative reweighted LS (IRLS) algorithm and the fast iterative shrinkage-thresholding (FIST) algorithm can be used to solve the prediction filter using the norm. The FIST algorithm uses the shrinkage-thresholding operator to promote the sparsity of estimated primaries and solves the predictive filter with iterative steps. Compared with the IRLS algorithm, the FIST algorithm can reduce the computation burden effectively while achieving similar accuracy. We have used the FIST algorithm for multichannel predictive deconvolution using the norm. Compared with traditional FIST-based single-channel predictive deconvolution and LS-based multichannel predictive deconvolution, our method can better balance primary preservation and multiple removal. Tests using synthetic and field data sets proved the effectiveness of the proposed method.