Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation, which allow e cient implementations of ECC. In this paper, we improve e cient algorithm for exponentiation on elliptic curves de ned over Fp in terms of a ne coordinates. The algorithm computes 2n2(2n1P +Q) directly from random points P and Q on an elliptic curve, without computing the intermediate points. Moreover, we apply the algorithm to exponentiation on elliptic curves with width{w Mutual Opposite Form (wMOF) and analyze their computational complexity. This algorithm can speed up the wMOF exponentiation of elliptic curves of size 160{bit about (21. 7%) as a result of its implementation with respect to a ne coordinates.