Fitting conic from images is a preliminary step for its plentiful applications. It's a common sense that geometric distance based fitting methods are better than algebraic distance based ones. However, for a long time, there has not been a geometric distance between a data point and a general conic that allows easy computation and achieves high accuracy simultaneously. In this paper, we derive a new geometric distance between a data point and a conic by revisiting Sampson distance. The new geometric distance is accurate and simultaneously still explicit analytical representation, which is greatly easy to be implemented. Then, based on the distance, a new cost function with combining Sampson distance is constructed. The conic fitting optimization by minimizing this cost function has all the merits of the geometric distance based methods and simultaneously avoids their limitations.