Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.