Elliptic Curve Cryptography (ECC) has become one of the research hotspots in cryptography in recent years. Scalar multiplication is the most crucial operation in ECC, and it largely determines the efficiency of ECC. To improve ECC's speed, we propose a new secure and efficient scalar multiplication algorithm on elliptic curves over GF(2^m). In addition, we present the new composite operation formulas 3P_1 and 2P_1 + P_2 using only x-coordinate, where P_1 and P_2 are points on an elliptic curve. To ensure the safety and efficiency of the proposed algorithm, we constitute an atomic block by adding dummy operations and using the Montgomery trick.