Abstract: The method ICCG. is one of the best iterative method for solving the system of linear algebraic equations, but it can only be applied to the symmetric and positive definite coefficient matrix. The TCG method itroduced in this paper is a modified ICCG mothod. It can be applied to the matrices which are non-singular、unsymmetric and not positive definite. For the unsteady problem this method can raise the efficiency by 18 percent as compared with tie ILU.CG method. In particular if we take the SIP incomplete L、U decomposition as the preconditioned method, TCG method can raise the efficiency by 40 percent. It is indeed a bast iterative method applied to the matrices which are unsymmetric and not positive definite. In this paper we deduce the TCG method with the elimination method as the incomplete L、U decomposition and use the computational results to indicate the reason why the TCG method converges more quickly than ILUCG method.