Concerning coupled algebraic Riccati equations arising from Markov jump linear-quadratic control problems, two iterative methods called the inexact Newton-MCG algorithm and the inexact Newton-OGP algorithm are proposed for the symmetric reflexive solution of those equations by making use of modified conjugate gradient algorithm and orthogonal projection algorithm as the inner iterative method, respectively. These two iterative algorithms have no other limits to the coefficient matrix except for the existence of symmetric reflexive solution. Numerical experiments confirm these two algorithms are effective.