This paper proposes a unified optimization framework to solve the time-parameterization problem of humanoid-robot paths. Even though the time-parameterization problem is well known in robotics, the application to humanoid robots has not been addressed. This is because of the complexity of the kinematical structure as well as the dynamical motion equation. The main contribution of this paper is to show that the time parameterization of a statically stable path to be transformed into a dynamically stable trajectory within the humanoid-robot capacities can be expressed as an optimization problem. Furthermore, we propose an efficient method to solve the obtained optimization problem. The proposed method has been successfully validated on the humanoid robot HRP-2 by conducting several experiments. These results have revealed the effectiveness and the robustness of the proposed method.