As a new type of learning machine developed on the basis of statistics learning theory, support vector machine (SVM) plays an important role in knowledge discovering and knowledge updating by constructing non-linear optimal classifier. However, realizing SVM requires resolving quadratic programming under constraints of inequality, which results in calculation difficulty while learning samples gets larger. Besides, standard SVM is incapable of tackling multi-classification. To overcome the bottleneck of populating SVM, with training algorithm presented, the problem of quadratic programming is converted into that of resolving a linear system of equations composed of a group of equation constraints by adopting the least square SVM(LS-SVM) and introducing a modifying variable which can change inequality constraints into equation constraints, which simplifies the calculation. With regard to multi-classification, an LS-SVM applicable in multi-classification is deduced. Finally, efficiency of the algorithm is checked by using universal Circle in square and two-spirals to measure the performance of the classifier.