Learning of a support vector machine (SVM) is formulated as a quadratic programming (QP) problem. Decomposition methods such as sequential minimal optimization algorithm and SVM^<light> are efficient iterative techniques for solving QP problems arising in SVMs. In each step, the decomposition method chooses a small number of variables and then solves the QP problem with respect to those selected variables. In this report, we propose a novel variable selection method based on conjugate gradient method and evaluate its effectiveness by using several benchmark data on both pattern classification and regression problems.