The inhomogeneous plasma parametric decay instability driven by frequency modulated pump is studied both theoretically and experimentally. A strong decrease of the threshold of decay instability of the Trivelpiece-Gould wave in a magnetized plasma is observed in a narrow range of the pump frequency modulation rates. The decay point motion due to the pump frequency modulation is shown to be responsible for this effect, which occurs when the decay point velocity is equal to the ion acoustic (IA) velocity. Effective instability suppression is demonstrated for larger decay point velocities. The time evolution of the decay wave amplitude is investigated for different pump frequency modulation rates.