Summary: This paper deals with the existence of a global solution for the weakly damped nonlinear wave with an exterior force in an anharmonic crystal: \[ u_{xt}+\tfrac 32 u_x^2u_{xx}+u_{xxxx}-\sin u+\varepsilon u_x=f. \] We first derive uniform a priori estimates in time, and then prove the existence of the global solution in \(H_0^1\cap H^2\).