It is crucial to study the axial compression behavior of concrete-filled steel tubular (CFST) columns to ensure the safe operation of engineering structures. The restriction between steel tubular and core concrete in CFSTs is complex and the relationship between geometric and material properties and axial compression behavior is highly nonlinear. These challenges have prompted the use of soft computing methods to predict the ultimate bearing capacity (abbreviated as Nu) under axial compression. Taking the square CFST short column as an example, a mass of experimental data is obtained through axial compression tests. Combined with support vector machine (SVM) and particle swarm optimization (PSO), this paper presents a new method termed PSVM (SVM optimized by PSO) for Nu value prediction. The nonlinear relationship in Nu value prediction is efficiently represented by SVM, and PSO is used to select the model parameters of SVM. The experimental dataset is utilized to verify the reliability of the PSVM model, and the prediction performance of PSVM is compared with that of traditional design methods and other benchmark models. The proposed PSVM model provides a better prediction of the ultimate axial capacity of square CFST short columns. As such, PSVM is an efficient alternative method other than empirical and theoretical formulas.