In this paper， the timing transmission gear of a certain type of domestic marine 20V diesel engine is taken as the research object. Aiming at solving the problem of frequent broken teeth fault， considering the influence of various types of internal and external comprehensive excitation， the lumped parametric bending-torsion coupling dynamic model of multi-branch gear transmission shaft system of diesel engine is established. Based on Newmark step-by-step integration method， the forced vibration response is predicted， and the accuracy of the model is verified by the actual test data. Considering the influence of dynamic load， the traditional tooth root bending stress load spectrum is modified， and the strength fatigue check of the faulty gear is carried out. The results show that the peak value of the response energy at the driven timing gear of the fuel supply cam end of the diesel engine is 5.2 timesthat of the peak value of the response energy at the flywheel end， which indicates that the speed fluctuation at the driven gear of the timing gear is too large and the torsional vibration characteristics are poor. At this time， the bending fatigue safety factor of the tooth root is only 1.35， which is in the general reliability range and is prone to tooth breakage. Based on the engineering practice experience， the vibration optimization design scheme of the fault gear transmission system is proposed to improve the bending fatigue