A convex quadratic programming (QP) problem is an optimization problem in which a convex quadratic function is minimized subject to some linear constraints. QP problems play important roles in many fields. Recently, the authors have proposed a two-phase sequential partial optimization algorithm for solving general convex QP problems, which is based on the decomposition method for the training of support vector machines. In this report, we describe the algorithm in detail and present experimental results to evaluate its performance.