A control system for a work vehicle includes a controller. The controller receives actual topography information of a work target. The controller determines a design surface that is positioned below the actual topography. The controller generates a command signal to move the work implement along the design surface. The controller determines if slip of the work vehicle has occurred. The controller raises the design surface when the blade tip of the work implement is positioned below an initial target surface when the slip occurs. The initial target surface is the design surface before the occurrence of the slip.