Fast point multiplication on a family of Koblitz elliptic curves in characteristic 3 is considered. Such curves are suitable for establishing provable secure cryptographic schemes with low bandwidth. By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method. The idea of the fast method is independent of the optimization of finite field arithmetic and the choice of coordinate expression for points of the elliptic curves.