The large heave motion of cylindrical FPSO is easy to cause instability of rocking motion and affect the safety of oil and gas production. Aiming at the strong coupling relationship between heave and pitch motion of cylindrical FPSO, established a two-degree-of-freedom nonlinear coupling motion equation. Based on the Perturbation Method, the approximate analytical solution of the equation is derived, and the heave and pitch coupling motion response and stability of the surge motion of platform are studied. The results show that the platform has good motion stability when the surge period is far away from the natural period of the platform heave. When the natural period of heave and pitch is close to 1:2 while the frequency of long-period swell is close to the heave natural frequency, the heave and pitch of the platform change from linear forced motion to 1/2 sub-harmonic motion. The amplitude of heave displacement has a nonlinear relationship with the amplitude of wave, and the pitch motion has a large response. When the platform undergoes internal resonance motion, increasing the heave damping can consume the energy of the heave resonance and reduce the amplitude of the heave motion. The increasing of the pitch damping reduces the amplitude of the pitch motion, meanwhile it will increase the minimum heave motion amplitude required to cause the heave energy to penetrate into the pitch motion, so the wave energy is concentrated in the heave mode, resulting in the raise of the amplitude of the heave motion.