Considering the influence of Rashba effect, which was brought by the spin-orbit interaction, the effective mass of bound polaron with strong-coupling between electron and phonon was expressed as a function of Rashba effect, speed and vibration frequency of polaron by using improved linear combination operator, LLP unitary transformation and variation methods. The numerical calculation results for RbCl quantum dot indicate that the effective mass and vibration frequency of bound polaron increase with increasing speed and confinement strength of polaron, as well as Coulomb bound potential, because of increasing of electronic kinetic energy with increasing polaron speed, enhancing interaction between electron and phonons with strengthening Coulomb bound potential, reducing effective range of electronic motion and increasing electronic kinetic energy with increasing confinement strength of polaron. The numerical calculation results also show that effective mass of bound poalron is split because of Rashba spin-orbit interaction, the splitting difference of effective mass decreases with increasing speed of polaron.