Abstract: A new method of conic fitting is presented in the paper.The method defines an objective function based on algebraic distance,and obtains six basic conics with six different constraints.The final fitting conic is produced by adding certain weights to coefficients of six basic conics.The examples for comparing the errors of fitting conics produced by the new method and other methods are included. Discussion has been also given in the paper to the geometric meaning of the objective function based on algebraic distance.