A ternary three-point approximating non-stationary subdivision scheme is presented that generates the family of C² limiting curve. The proposed scheme can be considered as the non-stationary counterpart of the ternary three-point approximating stationary scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing ternary three-point stationary scheme, which shows that the limit curves of the proposed scheme behave more pleasantly and are very close to generate the conic section.