Absolute value equation (AVE):Ax?|x|=b, where A is an n×n real matrix, arising in solving systems of interval linear equations. Linear complementarity problem, which subsumes many mathematical programming problems, can be formulated as an AVE. A semi-smooth Newton algorithm is proposed for solving the AVE. In the algorithm, two non-smooth equation reformulations are used. They are constructed based on the min- and FB-function, respectively. At each iteration, however, only one system of linear equations needs to be solved. The algorithm is globally and finitely convergent, under the condition that the interval matrix [A?I, A+I] is regular. The proposed algorithm was tested on 100 consecutively generated random instances of the AVE with n =1000. All of these test problems are well solved, with accuracy of 10?6.