The influence of phonon and megnetic field on property of polaron in quantum ring was studied by solving precisely the energy eigen-equation, unitary transformation and variational method. The numerical calculation for KBr quantum ring showed that the ground state energy of electron or polaron increases with increasing frequency (or the averaging radius) of the quantum ring, the polaron energy shift decreases with increasing frequency (or decreasing averaging radius) of the quantum ring, and the mean phonon number increases with increasing frequency (or decreasing averaging radius) of the quantum ring. When a perpendicular magnetic field is present, the energy levels of the polaron may cross, the ground state changes from the state with m=0 to that with m=-1,-2,-3,…, and the ground state energy makes non-periodical oscillation with increasing magnetic field strength; the polaron energy shift decreases with increasing magnetic field strength (or absolute value of quantum number |m|).