A controller calculates a virtual design surface including a first design surface extending from an excavation start position in a traveling direction of a work vehicle and a second design surface further extending from the first design surface in the traveling direction. The controller generates a command signal that causes the work implement to move along the virtual design surface. The controller changes a position of the first design surface so that the first design surface extends along the current landscape or is located below the current landscape when the first design surface is located above the current landscape.