Abstract: The statistical regression model widely used to predict the crack opening displacements of the concrete dams still has some shortcomings. Firstly, it is difficult to establish an effective statistical regression model for the observation time series of small sample size; secondly, the model fails to consider the residual term, which contains a large amount of information about crack development and evaluation. In order to accurately predict the crack opening, the residual terms should be included in the prediction model. At the same time, there is a chaotic component in the residual sequence of the statistical regression model, and the residual term is dominated by some dynamic characteristics. Based on the chaotic theory, the residual term is deduced and a mixed prediction model of statistics and chaos is developed. Specifically, the RLS (recursive least squares) adaptive prediction algorithm based on Legendre polynomials is used to propose a real-time prediction model for small sample observation data time series and a statistical regression-Legendre polynomial residual prediction model for large sample observation data time series. Finally, the real-time prediction model for the crack opening and the statistical regression- Legendre polynomial combination model are tested with the measured data of the crack opening at 105 m height of Chencun gravity arch dam. The calculation results show that the MLR-Legendre prediction model has good prediction accuracy and can provide some technical supports for the safe operation and management of the works. The model and the crack criterion established above can be used to describe objectively the actual status of the dam engineering.