The roller pushing mechanism has the advantages of simple structure,small size,pushing the material accurately,etc. It can be used in moving space is limited,where the robot is not easy to operate. The past and now known or unknown the information of position accuracy of roller pushing mechanism is regarded as a grey system. The regular testing error value of position accuracy of chain head is constituted as an original data series at equal intervals. The mathematical model of gray system is established. Monotonically increasing time data sequence is obtained by accumulating generating calculation. The albino form of differential equations of grey system GM（ 1,1） is established. Then the calculation accuracy is improved by correcting of residual model. The corrected GM（ 1,1） model is used to predict the life of the positional accuracy of the roller pushing mechanism.