Bubble departure frequency in film boiling on a stationary heating wall is in the order of a few hertz, which is interestingly the same as that for the natural frequency of a nuclear reactor building. Thus, the film boiling heat transfer of a nuclear fuel would be largely affected by system oscillation caused by low frequency earthquakes, and it is worth investigating the film boiling heat transfer for the heating wall in the oscillating system. To this end, multimode numerical simulations are performed for saturated film boiling on a horizontal surface in a system oscillating at low frequencies. There are three regimes in terms of heat transfer and bubble departure frequency. In the first regime, as the oscillation frequency increases, the heat transfer decreases while the bubble departure frequency remains nearly the same. In the second regime, as the oscillation frequency increases, the heat transfer decreases and the bubble departure frequency synchronizes with the oscillation frequency. In the third regime, as the oscillation frequency increases, the heat transfer increases and the bubble departure frequency synchronizes with the oscillation frequency.