Axially translating beams are widely seen in engineering applications. An active vibration control strategy based on a modified fuzzy sliding mode control is developed for controlling and stabilizing the motion of the beam. Geometric nonlinearity of the beam is considered. In the development of the control strategy, the governing equation of the beam is transformed into a multi-dimensional dynamic system with the Galerkin method of 6th order. An active control strategy is developed corresponding to the dynamic system, such that the control strategy can be used for multi-dimensional systems. Numerical simulations are performed with application of the control strategy developed. The effectiveness of the active control strategy is demonstrated in controlling and stabilizing the chaotic motion of the translating beam.