Directional Selective Fixed-Filter Active Noise Control (D-SFANC) can effectively attenuate noise from different directions by selecting the suitable pre-trained control filter based on the Direction-of-Arrival (DoA) of the current noise. However, this method is weak at tracking the direction variations of non-stationary noise, such as that from a moving source. Therefore, this work proposes a Predictive Directional SFANC (PD-SFANC) method that uses a Convolutional Recurrent Neural Network (CRNN) to capture the hidden temporal dynamics of the moving noise and predict the control filter to cancel future noise. Accordingly, the proposed method can significantly improve its noise-tracking ability and dynamic noise-reduction performance. Furthermore, numerical simulations confirm the superiority of the proposed method for handling moving sources across various movement scenarios, compared to several representative ANC baselines.