A nonlinear coupled vibration model of cables and bridge decks and towers and its 1∶2∶1 resonance was investigated. The cable was simplified as a concentrated mass jointed by two weightless strings. The deck and the tower were both simplified as a concentrated mass that can only move vertically and horizontally, respectively. By these simplifications, a nonlinear vibration system of three degrees of freedom was established. With the application of the method of multiple scales, the condition of occurrence of the internal resonance was obtained. The validity of the analysis was verified by numerical simulation. The results show that the 1∶2∶1 internal resonance will arise under some initial condition and then the vibration energy will be transformed and exchanged among the cables, the decks, and the towers regularly.