Strong nonlinear torsional vibration system of diesel shafting is studied. A dynamic model of torsional vibration system is established based on Lagrangian equation. Modified Lindstedt-Poincaré method is used to deal with primary resonance of diesel shafting torsional vibration of strong nonlinear system. Amplitude frequency response equation is obtained and influence of parameters on amplitude frequency response is analyzed. It shows that system frequency response exists jump phenomenon. As amplitude of harmonic torque decreases and damping increases, nonlinear jump of the system weakens, amplitude of the system reduces, and regions of primary resonance of the system decreases. With change of tuning parameter, amplitude excitation response has two kinds of topological structure. The result of MLP analysis is consistent with Runge Kutta numerical solutions.