This paper proposes a so called quasi-linear support vector machine (SVM), which is an SVM with a composite quasi-linear kernel. In the quasi-linear SVM model, the nonlinear separation hyperplane is approximated by multiple local linear models with interpolation. Instead of building multiple local SVM models separately, the quasi-linear SVM realizes the multi local linear model approach in the kernel level. That is, it is built exactly in the same way as a single SVM model, by composing a quasi-linear kernel. A guided partitioning method is proposed to obtain the local partitions for the composition of quasi-linear kernel function. Experiment results on artificial data and benchmark datasets show that the proposed method is effective and improves classification performances.