There is a lack of literature reporting the measurement and prediction of biochemical methane potential (BMP) of vegetable crop residues (VCRs) and similarly, the kinetic assessment on the anaerobic digestion process of VCR is rarely investigated. In this paper, the BMP tests of five different vegetable (snap bean, capsicum, cucumber, eggplant, and tomato) crop residues were conducted at feed to inoculum ratio (F/I) of 2.0 under mesophilic (36 ± 1 °C) conditions. A series of single-variable and multiple-variable regression models were built based on organic components (hemicellulose, cellulose, lignin, total fat, total sugar, and crude protein) for BMP prediction. Three kinetic models, including the first-order kinetic model, the Chen and Hashimoto model, and the modified Gompertz model, were used to simulate the methane yield results of VCR and obtain valuable model parameters simultaneously. As a result, the BMPs and volatile solids (VS) degradation degree of different VCRs were respectively in the range of 94.2–146.8 mL g⁻¹ VS and 40.4–49.9%; the regression prediction models with variables lignin (R² = 0.704, p = 0.076), variables crude protein and lignin (R² = 0.976, p = 0.048), and variables total fat, hemicellulose, and lignin (R² = 0.999, p = 0.027) showed the best performance on BMP prediction among the single-factor, two-factor, and three-factor models, respectively. In addition, compared to the other two kinetic models, the modified Gompertz model could be excellently fitted (R² = 0.986–0.998) to the results of BMP experiment, verification deviations within 0.3%.