In the process of preparing silicon single crystal, the Czochralski method has problems such as multiple mechanism assumptions, unclear boundary conditions under multiple field couplings, interlaced and mutual influence of physical and chemical changes, which makes it impossible to establish an accurate mechanism model for silicon single crystal growth process control. To solve this problem, based on a large amount of crystal growth data in the single crystal furnace pulling workshop, this paper analyzes the characteristic parameters related to crystal diameter based on the maximum information coefficient （MIC） algorithm proposed by the mutual information theory. Then, based on the nonlinear autoregressive with exogeneous inputs (NARX) dynamic neural network, a multiinput, and singleoutput equaldiameter phase crystal diameter prediction model was established, the diameter prediction was also performed for the three single crystal furnace pulling data, and the average mean square error value of the prediction is 0.000 774. Finally, the prediction model of crystal diameter in the equal diameter stage established based on the NARX dynamic neural network is compared with the prediction model of crystal diameter in the equal diameter stage established based on the back propagation (BP) neural network. The results of the comparative analysis verified the superiority of the NARX dynamic neural network model for predicting the crystal diameter in the isodiametric stage. The results show the NARX dynamic neural network provides a more accurate identification model for the control of crystal diameter.