Data prediction is one of the key problems for precision measurement and control. The data obtained by measuring system are often limited. To solve the small sample problem, the BP neural network methods are widely used. However, because of too many input factors and complex data training process, the convergence speed of the BP neural network method is slow. To increase the convergence speed, some grey relational analysis methods were introduced into the BP neural network methods. The grey relational coefficients were calculated first. And by sorting the grey relational coefficients, some factors with less relationship were removed form the BP neural network's inputs. Through the preliminary theory and experiment analysis, the data prediction under small sample could be fulfilled in accuracy and with high convergence speed.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.