The recently proposed twin parametric-margin support vector machine, denoted by TPMSVM, gains good generalization and is suitable for many noise cases. However, in the TPMSVM, it solves two dual quadratic programming problems (QPPs). Moreover, compared with support vector machine (SVM), TPMSVM has at least four regularization parameters that need regulating, which affects its practical applications. In this paper, we increase the efficiency of TPMSVM from two aspects. First, by introducing a quadratic function, we directly optimize a pair of QPPs of TPMSVM in the primal space, called STPMSVM for short. Compared with solving two dual QPPs in the TPMSVM, STPMSVM can obviously improve the training speed without loss of generalization. Second, a genetic algorithm GA-based model selection for STPMSVM in the primal space is suggested. The GA-based STPMSVM can not only select the parameters efficiently, but also provide discriminative feature selection. Computational results on several synthetic as well as benchmark datasets confirm the great improvements on the training process of our GA-based STPMSVM.