A rotational speed-reduction device is disclosed. The speed-reduction device includes a flange, a planetary bracket fixedly mounted on the flange, a planetary gear assembly movably mounted on the planetary bracket, a first bearing sleeved on the planetary bracket, an input member, and an output member. The planetary bracket includes a mounting portion, a fixing portion fixed to the flange, and a support portion. The support portion connects the mounting portion to the fixing portion. The planetary gear assembly includes a number of planetary gear pairs movably mounted between the fixing portion and the mounting portion, a fixing shaft passing through the planetary gear pairs, and rotation members movably received between the planetary gear pairs and sleeved on the fixing shaft. Opposite ends of the fixing shaft are connected to the mounting portion and the fixing portion, respectively.