For solving linear system of equations is known several algorithms. Iteration algorithms are recommended for the large linear systems with sparse matrix. But in the case of general non-symmetrical or n x m matrices the classic iterative algorithms are not applicable with a few exceptions. For example in some cases the Lanczos type algorithms are adequate. The algorithm presented here based on the minimization of square of residuum of approximate solution and it has some genetic character. Therefore this algorithm seems to be applicable for construction of parallel algorithm. Here we describe a parallel version of proposed algorithm and give its theoretical analysis. © 2006 Civil-Comp Press.