Because of the direct relation to every design phase of a ship, ship hull form is frequently designed by varying a well-made parent ship to avoid new design risks. In hull form variation, geometric satisfactory and good performance preservation of the parent ship are considered as the competing requirements. In order to perform the variation effectively, an appropriate compromise between these requirements should be accomplished. Instead of altering hull form parameters, we propose a flexible and intuitive approach to interactively vary hull surface with an arbitrary curve constraint and focus on preserving good properties of the original hull surface. The advantages of superposition of curve and surface is utilized to modify the hull shape. An intermediate surface, which satisfies an intermediate curve constraint and has a smooth shape, is conducted and superimposed on to the top of the original surface to yield the desired surface. A shape control mechanism using shape function simplifies control the surface modification with a curve constraint in a linear fashion way. The developed method is applied to modify a characteristic curve and a section line lying on the stern part of a container hull form. The changes of geometric shape and hydrodynamic performance due to the curve-constraint variation are assessed to demonstrate the practicality and efficiency of the proposed method.