Flutter stability is one of major concerns on the design of long-span cable-stayed bridges. Considering the geometric nonlinearity of cable-stayed bridges and the effects due to the nonlinear wind-structure interactions, a nonlinear method is proposed to analyze the flutter stability of cable-stayed bridges, and a computer program NFAB is also developed. Taking the Jingsha bridge over the Yangtze River as example, parametric analyses on flutter stability of the bridge are carried out, and some important design parameters that affect the flutter stability of cable-stayed bridges are pointed out.