The discovery of intrinsic magnetism in atomically thin two-dimensional transition-metal trichalcogenides has attracted intense research interest due to the exotic properties of magnetism and potential applications in devices. Pressure has proven to be an effective tool to manipulate the crystal and electronic structures of the materials. Here, we report investigations on ferromagnetic van der Waals Cr2Si2Te6 via high-pressure synchrotron x-ray diffraction, electrical resistance, Hall resistance, and magnetoresistance measurements. Under compression, Cr2Si2Te6 simultaneously undergoes a structural transition, emergence of superconductivity at 3 K, sign change of the magnetoresistance, and dramatic change of the Hall coefficient at ~8 GPa. The superconductivity persists up to the highest measured pressure of 47.1 GPa with a maximum Tc = 4.5 K at ~30 GPa. The discovery of superconductivity in the two-dimensional van der Waals ferromagnetic Cr-based Cr2Si2Te6 provides new perspectives to explore superconductivity and the interplay between superconductivity and magnetism.