A novel hyperbolic composite coupling is proposed. In addition to enjoying the advantages of composite materials, the proposed coupling can be readily integrated with composite drive shaft into a single unit. A mathematical model of the coupling is developed based on the Timoshenko beam theory using the energy approach and the extended Lagrange’s equations. The corresponding discrete equation of vibration is obtained using the finite element method and solved for the natural frequencies using MATLAB. The dynamic characteristics of the coupling (Axial, torsional and bending natural frequencies) are studied in order to assess the merits and potential of the proposed coupling.