With linear combination operator and variational method, the properties of strong-coupling magnetopolaron in a semiconductor quantum well are studied. The relations between the vibration frequency, ground state energy and self-trapping energy of the strong-coupling magnetopolaron in an infinite quantum well with the well width or the cyclotron resonance frequency are derived. Numerical results of the RbCl quantum well show that the vibration frequency, ground state energy and self-trapping energy of the strong-coupling magnetopolaron increase with increasing the cyclotron resonance frequency when the well width is given. The vibration frequency and self-trapping energy increase with increasing the well width and finally approach to the three-dimensional (3D) value of the bulk material in a determinate cyclotron resonance frequency, but the ground state energy decreases with increasing the well width, and when the well width is small, the quantum size effect is significant.