The research on the anthropomorphic flutist robot, at Waseda University, has focused on clarifying the human motor control while playing the flute, proposing novel applications for humanoid robots and enabling the communication with humans at the emotional level. As a result of our research, the flutist robot is able of nearly reproducing the basic technical skills required to play the flute. Furthermore, some of the extended technical skills have been roughly simulated by the robot. However, in order to enhance the expressiveness of the robot's performance, still further improvements are required. In particular, in this paper, we focus our research on understanding better how to enhance the expressiveness of the flute performance by studying in more detail the vibrato, which is believe to be one of the most important ways of expressing feelings/ideas while performing the flute. For this reason, the newest version of the flutist robot, the Waseda Flutist Robot No.4 Refined III has been developed by focusing on improving the design of the lung and designing of a human-like vocal cord mechanism, which are believed to have a close relation in producing vibrato. The details of the new mechanism are given and experiments were conducted to understand the effect of the movement of diaphragm and glottis while producing vibrato.