Cyclotron resonance (CR) in AlGaN/GaN two-dimensional electron system is investigated under high magnetic fields up to 15 T in order to study the magnetic field dependence of the electron effective mass. Non-linear dependence of the CR energy against the magnetic field is observed, indicating that the electron effective mass becomes heavier with increasing the magnetic field. This is partially due to the contribution from the resonant polaron effect because GaN has a large electron-longitudinal-optical (LO) phonon interaction among III-V compounds. The magnetic field dependence of the CR energy is explained well with the Fr¨ohlich polaron theory in the magnetic field.