Recently a new form of the extended Yule-Walker equations for a mixed autoregressive moving-average process of orders p and q has been proposed. It can be used to obtain p+q+1 parameter values from the first p+q+1 autocovariance terms. The autoregressive part of the equations is linear and can be easily solved. In contrast the moving-average part is composed of nonlinear simultaneous equations. Thus some iterative algorithms are necessary to solve them. The iterative algorithm presented by Choi(1986) is very simple but its convergence has not been proved yet. In this paper a Newton-Raphson solution for the moving-average parameters is presented and its convergence is shown. Also numerical example illustrate the performance of the algorithm.