Support vector machine (SVM) is a machine learning method based on structural risk minimization and can solve classification problems. However, with the complexity of research problems, the real classification problems are often multi-classification ones, whereas SVM can only be adopted to deal with binary classification tasks. To this end, the multiple birth support vector machine (MBSVM) combined with the one-against-all strategy can realize multi-classification with low complexity, but the classification accuracy is low. This study improves MBSVM and proposes a new SVM multi-classification algorithm which is a multiple birth support vector machine based on the hypersphere and fruit fly optimization algorithm with adaptive step size reduction (ASSRFOA). The algorithm is referred to as HA-MBSVM. Through the information obtained from hypersphere fitting, firstly all classes are divided into several blocks and then classifiers are constructed for each class. The constraint distance regulation factor is introduced to properly improve the difference of the classifiers. At the same time, ASSRFOA is employed to solve the quadratic programming problems and HA-MBSVM can better solve the multi-classification problems. Six datasets are utilized to evaluate the performance of HA-MBSVM. The experimental results show that the overall performance of HA-MBSVM is better than that of the comparison algorithms.