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A twin support vector machine (TWSVM) is an effective classifier, especially for binary data, which is defined by squared l₂-norm distance in the objective function. Since squared l₂-norm distance is susceptible to outliers, it is desirable to develop a revised TWSVM. In this paper, a new robust TWSVM via l_2,p-norm formulations was proposed, because it suppress the influence of outliers better than l₁-norm or squared l₂-norm minimizations. However, the resulted objective is challenging to solve, because it is non-smooth and non-convex. As an important work, we systematically derive an efficient iterative algorithm to minimize the pth order of l₂-norm distances. Theoretical support shows that the iterative algorithm is effective in the resolution to improve TWSVM via l_2,p-norm instead of squared l₂-norm distances. A large number of experiments show that l_2,p-norm distances twin support vector machine can treat the noise data effectively and has a better accuracy.