This article considers the problem of modeling a class of count time series with multiple change-points using segmented generalized integer-valued autoregressive (S-GINAR) processes. The minimum description length principle (MDL) is applied to study the statistical inference for the S-GINAR model, and the consistency results of the MDL model selection procedure are established respectively under the condition of known and unknown number of change-points. To find the “best” combination of the number of change-points, the locations of change-points, the order of each segment and its parameters, a genetic algorithm with simulated annealing is implemented to solve this difficult optimization problem. In particular, the simulated annealing process makes up for the precocious problem of the traditional genetic algorithm. Numerical results from simulation experiments and three examples of real data analysis show that the procedure has excellent empirical properties. •The S-GINAR model is proposed to model a class of non-stationary count time series.•Change-points estimation for the S-GINAR model based on the MDL criterion is studied.•The consistency theorems of parameters are discussed.•The Auto-SGINARM-SA procedure is proposed to solve the optimizing problems of change-points estimation.