The purpose of this study is to develop two predictive models for burr height in cutting titanium alloy plates by using Nd:YAG laser. Firstly, Taguchi method has been used to arrange the experimental scheme and analyze the results via analysis of mean. The important laser cutting parameters affecting burr height can be found. It shows that the pressure of assistant gas, the focusing position and the pulsed frequency are the most important cutting parameters in order. Then they have been chosen as the input variables for response surface methodology and used to construct a mathematical equation for predicting burr height. Secondly, the laser cutting parameters and experimental results obtained from conducting the schematic arrangement using Taguchi method and response surface methodology have been treated as training patterns and recalling patterns for the back-propagation neural network. As a result, a predictive model for burr height prediction in laser cutting titanium alloy has been established. To verify the accuracy of above two prediction models, there are 9 sets of experiment have been performed. It shows that the average error for predicting burr height by the mathematical equation derived from response surface methodology is 5.52% and by the predictive model established by back-propagation neural network is 4.51%, respectively. Obviously, both predictive models are good enough for the relational research and practical applications. It can be concluded that the procedure used in this research and the obtaining predictive models can be used practically in correlate industry.