A twin support vector machine (TWSVM) is an effective classifier, especially for binary data, which is defined by squared l ₂ -norm distance in the objective function. Since squared l ₂ -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 l ₁ -norm or squared l ₂ -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 l ₂ -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 l ₂ -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.