We demonstrated a new architecture of an electrowetting-on-dielectric (EWOD) device to transport a liquid droplet by the spatial modulation of an electric field produced using an embedded undulating electrode. The undulating electrode was constructed on an array of dielectric microstructures with different periods in region by region to generate a gradually varying lateral electric field. The contact angle of a droplet of water on the EWOD surface was found to decrease monotonically from 120 degrees to about 50 degrees with increasing the strength of the electric field. The transport of the water droplet was driven by the surface wettability gradient produced by means of the amplitude modulation of the electric field in space but not in time. Our EWOD configuration allows the flexibility in design, the simplicity in driving scheme, and the high accuracy in position for the liquid transport.