Abstract: In Miller's algorithm, the loop length plays an important role. By analyzing the loop control polynomial, the lower bound for the degree of some class of control polynomial is derived. Based on the lower bound, the method for selecting proper curve parameters for constructing pairing-friendly elliptic curve is proposed. Finally, when irreducible polynomial is used to generate pairing-friendly elliptic curve, the necessary and sufficient condition for the loop length reaching the lower bound is presented.