Abstract:A kind of new time series named Kaprekar series are created based on Kaprekar operation and Kaprekar constant to obtain chaos-like series with integer operation. Several analysis methods for time series are applied to research their characteristics, including Power Spectral Density(PSD), phase space construction, maximal Lyapunov exponents and Principal Component Analysis(PCA) and so on. Through cyber-simulation and the comparison with Logistic series, the chaos-like characteristics of Kaprekar series are validated. Kaprekar series are then applied to image encryption, and good results are obtained in image encryption experiments.