Abstract Model selection is an important problem of costsensitive SVM (CS-SVM). Although using solution path to find global optimal parameters is a powerful method for model selection, it is a challenge to extend the framework to solve two regularization parameters of CS-SVM simultaneously. To overcome this challenge, we make three main steps in this paper. (i) A critical-regions-based biparameter space partition algorithm is proposed to present all piecewise linearities of CS-SVM. (ii) An invariant-regions-based bi-parameter space partition algorithm is further proposed to compute empirical errors for all parameter pairs. (iii) The global optimal solutions for K-fold cross validation are computed by superposing K invariant region based bi-parameter space partitions into one. The three steps constitute the model selection of CS-SVM which can find global optimal parameter pairs in K-fold cross validation. Experimental results on seven normal datsets and four imbalanced datasets, show that our proposed method has better generalization ability and than various kinds of grid search methods, however, with less running time.