Considering that robust L1-norm Non-parallel Proximal Support Vector Machine (L1-NPSVM) can not guarantee a reliable solution, a new iterative algorithm was proposed to solve the objective of L1-NPSVM. Since the objective problem of L1-NPSVM is invariant to the scale of solution, such that it can be transformed into a maximization problem with an equality constraint. And then the proposed iterative algorithm was used to solve it. The iterative algorithm in each iteration obtained updated solution of each iteration by using weight updating mechanism, and the problem was reduced to solve two fast linear equations in each iteration. The convergence of the algorithm was proved theoretically. Experiments on the common UCI datasets show that the proposed algorithm is not only superior to L1-NPSVM in classification performance, but also has considerable computational advantage.