Abstract: A class of convergent difference schemes with several parameters is proposed.According to the relationship between the subdivision scheme and its difference scheme and the sufficient condition for C^k continuity,we can devise curve subdivision schemes with arbitrary order continuity.By setting appropriate parameters,some classical curve subdivision schemes such as the Chaikin's scheme,the cubic B-spline scheme and 4-point interpolating scheme can be obtained.A C¹-continuous asymmetric 3-point interpolating scheme is also presented to model asymmetric limit curves.Furthermore,the property of the linear combination of the difference schemes of the same order is analyzed,which can help to devise more convergent curve subdivision schemes with several parameters.