The large heave motion of cylindrical Floating Production Storage and Offloading (FPSO) is easy to cause instability of rocking motion and affect the safety of oil and gas production. Aimed at the strong coupling relationship between heave and pitch motion of cylindrical FPSO, a two-degree-of-freedom nonlinear coupling motion equation is established. Based on the perturbation method, the approximate analytical solution of the equation is derived, and the coupled heave-pitch motion response and stability of the cylindrical FPSO are studied. The results show that: the platform is of good motion stability when the swell period is far away from the natural heave period of the cylindrical FPSO; when the natural period ratio of heave to pitch is close to 1?2 while the frequency of long-period swell is close to the natural heave frequency, the heave and pitch of the cylindrical FPSO change from linear forced motion to 1/2 subharmonic motion; the amplitude of heave displacement is of a nonlinear relationship with the amplitude of wave, and the pitch motion is of a larger response; when the cylindrical FPSO 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 can reduce the amplitude of the pitch motion, meanwhile it will increase the minimal 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.