On the basis of Lee-Low-Pines unitary transformation, the properties of strong-coupling magnetopolarons in quantum disks (QDs) induced by the Rashba spin-orbit interaction are studied using the Tokuda improved linearly combined operator method. Results show that the state properties of magnetopolarons are closely linked with the sign of the interaction energy Eint, and the Eint of magnetopolarons changes with the transverse confinement strength 0, the cyclotron frequency of the external magnetic field c, the electron-LO phonon coupling strength , and the thickness L of QDs. The average number N of phonons increases with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. The effective mass m0* of magnetopolarons splits into two (m+*, m-*), induced by the Rashba spin-orbit interaction, and the values of them increase with increasing c, 0 and , but the oscillation decreases with increasing thickness L of QDs. For the ground state of magnetopolarons in QDs, the electron-LO phonon interaction plays a significant role, meanwhile, the Rashba spin-orbit coupling effect cannot be ignored. Only for the lower volocity of the electrons, can the polaron effect and the Rashba spin-orbit interaction effect on the magnetopolaron be obvious.