We theoretically investigate the spin relaxation of polaron, which arises from the electron interactions with the longitudinal optical phonon between the sublevel Zeeman splitting of the polaron ground state by using the vibrational and the unitary transformation methods in a two-dimensional quantum dot, where the Rashba spin-orbital coupling is taken into account. In fact, this process occurs by means of the absorption (or emitting) of a deformation potential acoustic phonon (or a piezoelectric one). The relaxation rate dependences of the magnetic, the quantum dot radius, the lander parameter, the Rashba spin-orbital coupling parameter are studied under the conditions of the strong coupling limitation and the weak one.