We apply a three-step sequential procedure to estimate the change-point of count time series. Under certain regularity conditions, the estimator of change-point converges in distribution to the location of the maxima of a two-sided random walk. We derive a closed-form approximating distribution for the maxima of the two-sided random walk based on the invariance principle for the strong mixing processes, so that the statistical inference for the true change-point can be carried out. It is for the first time that such properties are provided for integer-valued time series models. Moreover, we show that the proposed procedure is applicable for the integer-valued autoregressive conditional heteroskedastic (INARCH) models with Poisson or negative binomial conditional distribution. In simulation studies, the proposed procedure is shown to perform well in locating the change-point of INARCH models. And, the procedure is further illustrated with empirical data of weekly robbery counts in two neighborhoods of Baltimore City.