Abstract: Algorithms of the block multisplitting and preconditioned Krylov iterative Method for linear systems of the form Ax=f are proposed,where A is block tridiagonal matrix. The convergence of these iterative methods is analysed,when A is an M matrix or H matrix.The resulting MPPE method and preconditioned AKrylov method have been tested on a Challenge L computer.Numerical examples indicates that the new method is very efficient,since the parallel computation can be applied.