Blast furnace slag (BFS) and fly ash (FA), as mining-associated solid wastes with good pozzolanic effects, can be combined with superplasticizer to prepare concrete with less cement utilization. Considering the important influence of strength on concrete design, random forest (RF) and particle swarm optimization (PSO) methods were combined to construct a prediction model and carry out hyper-parameter tuning in this study. Principal component analysis (PCA) was used to reduce the dimension of input features. The correlation coefficient (R), the explanatory variance score (EVS), the mean absolute error (MAE) and the mean square error (MSE) were used to evaluate the performance of the model. R = 0.954, EVS = 0.901, MAE = 3.746, and MSE = 27.535 of the optimal RF-PSO model on the testing set indicated the high generalization ability. After PCA dimensionality reduction, the R value decreased from 0.954 to 0.88, which was not necessary for the current dataset. Sensitivity analysis showed that cement was the most important feature, followed by water, superplasticizer, fine aggregate, BFS, coarse aggregate and FA, which was beneficial to the design of concrete schemes in practical projects. The method proposed in this study for estimation of the compressive strength of BFS-FA-superplasticizer concrete fills the research gap and has potential engineering application value.