Dynamic response characteristics of the passive heave compensator with auxiliary gas bottles are investigated in this paper. A mathematical model of the passive heave compensator is developed which includes mechanics, hydraulics and pneumatics. The key innovation of the proposed model is that the thermodynamic model of gas exchange between the piston accumulator and the gas bottles is derived and discussed. Meanwhile, a one-dimensional model of the pipeline resistance effect is established to calculate the pressure drop across the oil pipeline. The proposed model is used to evaluate the different design parameters of the passive heave compensator for heavy lifting cranes. A study was conducted to investigate the influence of the design parameters on the effectiveness of the passive compensator to reduce the payload displacement. The simulation results indicated that substantial improvement may be possible by careful design parameter selection and optimization.