How to choose suitable degree of fitting implicit polynomial curves and surfaces is a key problem when the objects are described and recognized by implicit polynomials, but the problem is not solved in theory. A theorem is presented to determine the degree of fitting implicit polynomials based on the object boundary features, and the formula for the degree of fitting implicit polynomial is given. From the theory, the algorithm for determination of the degree of implicit polynomials is followed: detecting the stationary points in the object boundary based on its features, and then calculating the minimum degree according to the formula derived from the theorem. In addition, the theory can be extended to three-dimensional object. Finally, experiments are given to illustrate the efficiency and operation of the algorithm.