Paving compaction has an important influence on the significant improvement of the asphalt mixture density during pavement construction, and the paving density is mainly affected by the paver response and material behavior. To improve the density of asphalt pavement, this paper proposes a nonlinear dynamic vibration system of the interaction between asphalt mixture and screed plate. Based on the harmonic balance principle, a multi-degree of freedom nonlinear system of the screed plate-asphalt mixture interaction was established. By considering material characteristics and energy absorption efficiency during paving compaction, a paving density tendency-vibration frequency theoretical model was applied to analyze the influence law of dynamic response of the asphalt-screed interaction on the material density. The analysis results indicated that 1) both the characteristics of the asphalt mixture and the vibration frequency of the screed affected the material density during the paving process; 2) the optimal vibration frequency was higher than the natural frequency, and further compaction with a lower vibration frequency can effectively improve the energy absorption efficiency; 3) for the screed in movement, only when the vibration frequency enters the resonance region of the high-density mixture can a better compaction effect be obtained. Finally, the nonlinear dynamic model was experimentally verified. The research results are beneficial for improving the paving density and the quality of asphalt pavement, providing a basis for the effective compaction of asphalt pavement.