In this paper, a new linear programming formulation of a 1-norm twin support vector regression is proposed whose solution is obtained by solving a pair of dual exterior penalty problems as unconstrained minimization problems using Newton method. The idea of our formulation is to reformulate TSVR as a strongly convex problem by incorporated regularization technique and then derive a new 1-norm linear programming formulation for TSVR to improve robustness and sparsity. Our approach has the advantage that a pair of matrix equation of order equals to the number of input examples is solved at each iteration of the algorithm. The algorithm converges from any starting point and can be easily implemented in MATLAB without using any optimization packages. The efficiency of the proposed method is demonstrated by experimental results on a number of interesting synthetic and real-world datasets.