Within the framework of relativistic mean field theory- the Dirac equation of electrons in solid states, the electron spin dynamics and the related problems are discussed.Firstly, we discuss the high-order effects of electron spin dynamics by virtue of non-relativistic expansion of the Hamiltonian for large component of Dirac equation, the electron spin dynamics Hamiltonian including the first-order and second-order Rashba effects have been derived. In the case of two-dimension and perpendicular constant electric field, the corresponding eigenenergies and eigenfunctions of the spin dynamics Hamiltonian are obtained. Finally, the physical meaning and the magnitude of the correction of the second-order Rashba effect are discussed.