The method of the harmonic oscillator operator algebra has been used to study the two-dimensional polaron in a magnetic field. Both the surface optical phonon and the surface acoustic phonon, and their interaction with the magnetic field are included. Ground-state energy corrections up to fourth-order perturbation for limiting cases of strdng field and that in second-order perturbation for field of arbitrary strength are derived. It is found that the surface acoustic phonon makes a significant contribution to ground-state energy of a two-dimensional polaron in magnetic field.