This paper first makes a study of the shape variation laws of generic planar parametric curves by means of geometry deformation, obtains a necessary and sufficient condition for a curve's occurring inflection points and a functional equation to determine the inflection points on the deforming curves. Then based on the results, the paper puts forward a method to study the inflection points on NURBS of non-convex control polygon, particularly makes an investigation on the distribution of inflection points on the curve whose control polygon is regular and with one to two inflection points, and gains several conditions and criterions for analysis and manipulation of the respected NURBS curves. The results are useful for the algorithm-design and shape-control in CAD modeling.