Spectrum anomaly detection is of great importance in wireless communication to secure safety and improve spectrum efficiency. However, spectrum anomaly detection faces many difficulties, especially in unauthorized frequency bands. For example, the composition of unauthorized frequency bands is very complex and the abnormal usage patterns are unknown in prior. In this paper, a noise attention method is proposed for unsupervised spectrum anomaly detection in unauthorized bands. First of all, we theoretically prove that the anomalies in unauthorized bands will raise the noise floor of spectrogram after VAE reconstruction. Then, we introduce a novel anomaly metric named as noise attention score to more effectively capture spectrum anomaly. The effectiveness of the proposed method is experimentally verified in 2.4 GHz ISM band. Leveraging the noise attention score, the AUC metric of anomaly detection is increased by 0.193. The proposed method is beneficial to reliably detecting abnormal spectrum while keeping low false alarm rate.