Taking the sliding bearing into account, the lateral vibration analysis models of two single rotor were built respectively using the transfer matrix method. The transmission matrix of herringbone gearcoupled unit is derived. Using whole transfer matrix method, the lateraltorsional coupling analysis model of herringbone gearrotor system is set up, and the vibration characteristics of gearrotorbearing system in gas turbine is analyzed. Through numerical calculation and anlysis, the eigenvalue of gearrotor system, the Logarithmic decrement and the critical speed are obtained. The result shows that the working speed of this gearrotorbearing system is far away from the critical speed, therefore the system is stable and safe.