The properties of magnetopolaron in asymmetry quantum well is studied by Pekar variation method. The ground state energy of magnetopolaron is derivated theoretically, and the relationship between ground state energy of magnetopolaron and wave vector, well width, magnetic field cyclotron resonance frequency and well depth is discussed respectively. It is shown that the magnetopolaron ground state energy is an increasing function of the wave vector and the magnetic field cyclotron resonance frequency, but a decreasing function of the well width and well depth. Due to the inversion asymmetry of crystal structure and the effect of magnetic field, the polaron energy will undergo Rashba spin-orbit splitting and Zeeman splitting. The dominant position of Rashba effect and Zeeman effect under the strong and weak magnetic fields is discussed respectively. Since the existence of phonons reduces the total energy of polarons, the polaron state is more stable than the bare electron state, and its energy splitting is also more stable.