Nanomagnetic oscillator is a key component for radio-frequency (RF) signal generation in many nano-scale spintronic devices. However, the actuation mechanisms of nanomagnetic oscillators are mostly current-based, which is energy inefficient at nanoscale due to Joule heating. In this study, we present a new actuation mechanism for nanomagnetic oscillator with pure voltage input using a multiferroic structure. An AC voltage with a DC bias is applied to the piezoelectric substrate, and steady perpendicular magnetic oscillation is achieved in the attached Ni disk when the frequency of the voltage matches the ferromagnetic resonance (FMR) of the Ni disk. The FMR can be tuned by simply changing the voltage bias, therefore, the oscillation frequency has a wide range. A systematic simulation study is conducted to investigate the impact of the voltage amplitude, frequency, waveform, as well as the thickness of the magnet on the magnetic oscillation. This opens new possibilities of designing energy efficient nanomagnetic oscillators using multiferroics that have large amplitude and wide frequency range.