The influence of the Rashba spin-orbit interaction (SOI) and longitudinal optical (LO) phonon effect on the ground-state properties of the Fr¨ohlich bipolaron in a quantum dot are studied using the Tokuda-modified linear-combination operator method based on the Lee-Low-Pines unitary transformation. The results indicate that, under the condition of strong electron-phonon coupling (coupling strength > 6), Eint < 0, the electron-phonon coupling body in quantum dot is mainly the bipolaron which is in a stably bound state. The bipolaron interaction energy Eint increases with increasing confinement strength of the quantum dot !0, electron-phonon coupling strength , and polaron velocity u and decreases with increasing Coulomb confinement potential and Rashba spinobit coupling strength R. In the bipolaron interaction energy Eint, the electron-phonon coupling energy Ee−ph plays the leading role, followed by the confinement potential energy of the quantum dot Ecoul and the Coulomb interaction energy between two electrons Ecouf . Though the additional energy ER−ph caused by the phonon effect accounts for a smaller percentage than the previous three, the electron-phonon coupling and the Rashba spin-obit coupling influence and infiltrate each other. Therefore, the influences of the bipolaron effect and the Rashba electron-spin interaction cannot be ignored when studying a quantum dot.