In the process of solving radiation hydrodynamics, the non-physics results often leads to the failure of the solution. In this paper, for radiation hydrodynamics based on maximum entropy approximation under the condition of one-dimensional spherical symmetry, the positive schemes of the operator splitting method are given; the calculation method of spherical symmetric source term is improved, and the time step limitation is reduced; the reconstructing Eddington factor is used instead of the direct reconstructing radiation flux to avoid the non-physics results brought by the reconstructing process. Finally, some examples are given to verify the correctness of the method.