Voltage-induced motion of a magnetic domain wall (DW) has potential in developing novel devices with ultralow dissipation. However, the speed for the voltage-induced DW motion (VIDWM) in a single ferromagnetic layer is usually very low. In this work, we proposed VIDWM with high speed in a synthetic antiferromaget (SAF). The velocity for the coupled DWs in the SAF is significantly higher than its counterpart in a single ferromagnetic layer. Strong interlayer antiferromagnetic exchange coupling plays a critical role for the high DW velocity since it inhibits the tilting of DW plane with strong Dzyaloshinskii-Moriya interaction. On the other hand, the Walker breakdown of DW motion is also inhibited due to the stabilization of moment orientation under a strong interlayer antiferromagnetic coupling. In theory, the voltage-induced gradient of magnetic anisotropy is proved to be equal to an effective magnetic field that drives DW.