Abstract: This paper utilizes the column action method with the greedy method and the dividing-Conquering strategy to put forward a message passing multiple instruction stream-multiple data stream (MIMD) parallel iterative method for determining the solution of arbitrary consistent band system of linear equations or the least squares solution of arbitrary inconsistent band system of linear equations, also analyzes its convergence and its computational complexity, so its numerical stability. Moreover, the method in this paper con make roughly balance of the computation workload to each processor, hence can obtained ideal speed-up and parallel efficiency.