Nonlinear damping rates of finite amplitude electrostatic waves are obtained by using an invariant perturbation method. The result is valid in an initial phase defined by 0<t≲tb≡r/wb(wbis the bounce frequency). As e‖f‖/T(f is the wave potential, andTis the temperature) increases, the nonlinear initial damping becomes significant and it dominates the linear damping rate glwhen, for example,e‖f‖/T≳0.3 fork= 0. 2kD(kDthe Debye shielding constant) ande‖f‖/T≳0.7 fork= 0.3kD. The theory does not assume a constant slope of the velocity distribution functionf0at the phase velocityvpsince higher order derivatives off0atvp, ∂nf0/∂vpn(n= 3,5) play an essential role in enhanced damping. First, a dispersion relation is obtained, is solved for the Langmuir wave, and the theory is applied to an ion‐acoustic wave. A simulation study is carried out on the latter wave. The result confirms the validity of the theory.