In traditional fuzzy support vector machine(FSVM), membership function is established in global scope will reduce the membership of support vectors, and the FSVM based dismissing margin increases the training speed, but will remove some support vector artificially. So, a new algorithm of Fuzzy Support Vector Machine with Dual Membership based on Hypersphere (HDM-FSVM) is proposed. In this algorithm, the two classes of hyperspheres are divided into two parts respectively. Then, according to most support vectors are in the hemispheres which close together, we use the membership function that can enhance the membership of support vector, and because of there are a few of support vectors in other hemispheres, we must ensure the high membership of support vectors and reduce the membership of non-support vector. In order to removal noise and outliers, we introduce a radius controlling factor to control size of hyperspheres, the samples that outside of hyperspheres are considered as noise and outliers. Experimental results show that HDM-FSVM can enhance the classification accuracy rate of the sample sets that contain noise and outliers.