In this paper, we consider an algebraic additive Schwarz iteration scheme for solving the 6nite-dimensional linear complementarity problem that involves an M-matrix. The scheme contains some existing algorithms as special cases. We establish monotone convergence of the iteration scheme under appropriate conditions. Moreover, using the concept of weak regular splitting, we estimate weighted max-norm bounds for iteration errors; thereby we show that the sequence generated by the iteration scheme converges to the unique solution of the problem without any restriction on the initial point.