The dynamic analysis of the multi-shaft turbine rotor equipped with a spur gear pair for the various gear parameters is studied. Main components of the multi-shaft turbine rotor system include the outer shaft, the inner shaft, the impeller shaft, the oil shaft and the ball bearings. The global assumed mode method (GAMM) is applied to model the rotor motion and the system equation of motion is formulated using Lagrange's approach. The dynamic behavior of the geared multi-shaft turbine rotor system includes the natural frequency, mode shape and unbalanced response. Numerical results show that large vibration amplitude is observed in steady state at self-excited rotating speed adjacent to the natural frequency. There is no influence of the various pressure angle, modulus, and modification coefficients on unbalance response. Contrary to above cases, the variation of the system unbalance response is dominated by the tooth types rather than the other gear parameters.