Abstract Due to the strong nonlinear relationship between the shape and roundness of the roller and the grinding process parameters, a prediction method for roll shape error and roundness error based on an improved Elman neural network is proposed. During the training process of the Elman neural network, Sine chaotic mapping is used to make the population distribution more uniform, and the sparrow search algorithm is used to obtain the optimal parameters of the Elman neural network. The verification results show that the prediction errors of the roll shape and roundness are both less than 10%, and the accuracy of the prediction model is higher than 85%, which proves the effectiveness of the proposed method.