Selective video encryption effectively preserves privacy by allowing resource-constrained client devices to outsource sensitive video data to cloud servers for processing, such as in privacy-preserving intelligent early warning systems for home surveillance. However, existing anomaly detection methods in encrypted videos still exhibit a significant performance gap compared to plaintext-based methods. To tackle this challenge, we introduce an innovative training method for anomaly detection models in encrypted videos, designed to improve detection performance and offer new insights into training anomaly detection models in encrypted videos using knowledge distillation. Concretely, we utilize a pre-trained plaintext model as the teacher model, generating soft labels to guide the training and optimization of the student model in encrypted videos. Experimental results demonstrate that our method improves performance on the UCF-Crime and XD-Violence datasets by approximately 7% and 5%, respectively, compared to the existing privacy-preserving state-of-the-art methods.