It is very important to study displacement prediction in geotechnical engineering. Nowadays, the grey system method, time series analysis method and artificial neural network method are three main methods. Based on the brief introduction, the three methods are analyzed comprehensively. Their merits and demerits, applied ranges are revealed. To solve the shortcomings of the artificial neural network method, a new prediction method based on new evolutionary neural network is proposed. Finally, through two real engineering applications, the analysis of three main methods and the new evolutionary neural network method all have been verified. The results show that, the grey system method is a kind of exponential approximation to displacement sequence, and time series analysis is linear autoregression approximation, while artificial neural network is nonlinear autoregression approximation. Thus, the grey system method can suitably analyze the sequence, which has the exponential law, the time series method can suitably analyze the random sequence and the neural network method almostly can be applied in any sequences. Moreover, the prediction results of new evolutionary neural network method is the best, and its approximation sequence and the generalization prediction sequence are all coincided with the real displacement sequence well. Thus, the new evolutionary neural network method is an acceptable method to predict the measurement displacements of geotechnical engineering.