This paper deals with an optimal ZMP based pattern generator for stable dynamic walking. The proposed method is based on a Three-Mass Linear Inverted Pendulum Model (3MLIPM) which is used as a simplified dynamic model of the biped robot. Indeed, 3MLIPM simplifies the biped robot as a three point masses and two links system. A ZMP criterion is used in an optimization problem to find the best values of the model's parameters for different walking gaits. Numerical simulations are introduced to show the effectiveness of the proposed pattern generator for straight walking as well as for walking direction change.