Most green plums need to be processed before consumption, and due to personal subjective factors, manual harvesting and sorting are difficult to achieve using standardized processing. Soluble solid content (SSC) of green plum was taken as the research object in this paper. Visible near-infrared (VIS-NIR) and shortwave near-infrared (SW-NIR) full-spectrum spectral information of green plums were collected, and the spectral data were corrected and pre-processed. Random forest algorithm based on induced random selection (IRS-RF) was proposed to screen four sets of characteristic wavebands. Bayesian optimization CatBoost model (BO-CatBoost) was constructed to predict SSC value of green plums. The experimental results showed that the preprocessing method of multiplicative scatter corrections (MSC) was obviously superior to Savitzky–Golay (S–G), the prediction effect of SSC based on VIS-NIR spectral waveband by partial least squares regression model (PLSR) was obviously superior to SW-NIR spectral waveband, MSC + IRS-RF was obviously superior to corresponding combination of correlation coefficient method (CCM), successive projections algorithm (SPA), competitive adaptive reweighted sampling (CARS), and random forest (RF). With the lowest dimensional selected feature waveband, the lowest VIS-NIR band group was only 53, and the SW-NIR band group was only 100. The model proposed in this paper based on MSC + IRS-RF + BO-CatBoost was superior to PLSR, XGBoost, and CatBoost in predicting SSC, with R2P of 0.957, which was 3.1% higher than the traditional PLSR.