During the communication and interaction with a human using motions or gestures, a humanoid robot needs not only to look like a human but also to behave like a human to make sure the meanings of the motions or gestures. Among various human-like behaviors, arm motions of the humanoid robot are essential for the communication with people through motions. In this work, a mathematical representation for characterizing human arm motions is first proposed. The human arm motions are characterized by the elbow elevation angle which is determined using the position and orientation of human hands. That representation is mathematically obtained using an approximation tool, Response Surface Method (RSM). Then a method to generate human-like arm motions in real time using the proposed representation is presented. The proposed method was evaluated to generate human-like arm motions when the humanoid robot was asked to move its arms from a point to another point including the rotation of its hand. The example motion was performed using the KIST humanoid robot, MAHRU.