Effects of speed of polaron on properties of a strong-coupling magneopolaron in a quantum dot are studied by using improved linear combination operator and the unitary transformation methods. Relations of the vibrational frequency, ground state energy, effective mass and interaction energy of a strong-coupling magnetopolaron considering the influence of Rashba effect, which is brought by the spin-orbit interation, are derived in the quantum dots with speed of polaron. Numerical calculations for RbCl crystal are performed and the results show that the vibration frequency, ground state energy and effective mass of the strong-coupling magnetopolaron in a quantum dot increase with increasing of speed of poloran, and interaction energy of magnetopolaron decreases.