This chapter proposes an accelerated decomposition algorithm for robust support vector machine (SVM). Robust SVM aims at solving the overfitting problem when there is outlier in the training data set, which makes the decision surface less detored and results in sparse support vectors. Training of the robust SVM leads to a quadratic optimization problem with bound and linear constraint. Osuna provides a theorem which proves that the Standard SVMs Quadratic Programming (QP) problem can be broken down into a series of smaller QP sub-problems. This chapter derives the Kuhn-Tucker condition and decomposition algorithm for the robust SVM. Furthermore, a pre-selection technique is incorporated into the algorithm to speed up the calculation. The experiment using standard data sets shows that the accelerated decomposition algorithm makes the training process more efficient.