The deformation of cloth is one of the essential aspects to increase the sense for the real in the area of VR(Virtual Reality)or game programming. In contrast, when a character wearing clothes or hanging a flag moves abruptly and rapidly, it's not quite easy to express the natural movement of the cloth in a limited time. In this paper, the position-based approximation method that considers the non-linearity which is a vital feature in the realistic deformation of cloth and responds stable to the abrupt and frequent external forces as well is proposed. Our method that processes the non-linear deformation properties geometrically can produce a fast and stable cloth animation. In addition, it reflects the physical attributes to the geometrical relation so that the visibly-plausible movement of cloth an be generated. As a result, cloth animation that is stable despite of fast movement of a car and realistic to the external environmental change such as the driving direction of the car or the surface of the road, an be created.