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We study the probability density and the excitation energy of the bound polaron in the quantum pseudodot under the Rashba spin–orbit interaction by using the unitary transformation of Lee–Low–Pines and the variational method of Pekar. The results of a numerical calculation show that the probability density of the bound polaron in the superposition state is periodic and oscillates with the period T 0. Due to the Rashba spin–orbit interaction, the excitation energy splits into different branches. It also can be seen that the excitation energy changes with the phonon wave vector when the two-dimensional electron gas's chemical potential, the electron–LO phonon coupling, the Coulomb bound potential and the Rashba coupling parameter take different values. • Periodicity of probability density with space–time coordinate has been discussed. • Rashba effects on excitation energy of bound polaron in QPD have been investigated. • Unitary transformation of Lee–Low–Pines and variational method of Pekar are used. • Excitation energy increases with phonon wave vector even if other parameters take different values. • The excitation energy can be adjusted by the wave vector, etc. [ABSTRACT FROM AUTHOR]