In computer vision and digital image processing it is an important task to estimate an ellipse most fitting a set of points. An ellipse is specified by nonlinearly constrained parameters, which are difficult to be reflected in a criterion function. We show that iterative processes are useful to solve problems in such a case, and propose an iterative procedure to fit an ellipse to a set of points. In the procedure the nonlinear constraints on parameters are represented by a properly defined nonlinear operator. Experimental results on personal computer indicate the effectiveness of the procedure.