Nonlinear dynamic behaviors of the viscoelastic arch described by fractional-order differential are presented in this paper.The background of the research is based upon two engineering practices.One is that the visco-elastic features of some advanced polymeric materials can be accurately modeled by fractional calculus constitutive law.The other, both geometrical and material nonlinearity of some arches can not be neglected in many cases such as the vibration with large displacement or large strain and the vibration control by means of polymeric dampers.The simplified Duffing-like model of the arch with nonlinear damping described by fractional derivative constitutive law was carefully studied here.The results show that because of both geometrical nonlinearity and nonlinear damping the chaotic vibration of the arch appears evidently in forced vibration.And the stronger damping from nonlinear fractional derivative obviously affects the dynamic behavior of nonlinear fractional differential arch.