Anomaly detection from hyperspectral images (HSI) is an important task in the remote sensing domain. Considering the three-order characteristics of HSI, many tensor decomposition based hyperspectral anomaly detection (HAD) models have been proposed and drawn much attention during the past decades. However, as most tensor decomposition based detectors are directly performed on the original HSI, the detection accuracy is usually limited due to the high-dimension and noise corruption of the HSI. Benefiting from the good capacity of autoencoders (AE) for feature extraction, in this article, an enhanced tensor decomposition-inspired convolutional AE for HAD is proposed to address those problems, named TDNet. Within the proposed TDNet, the traditional canonical-polyadic (CP) tensor decomposition model is innovatively alternated by a deep neural network (DNN), and the DNN tensor decomposition model performs more stably and robustly for noise. Specifically, a potential abnormal pixels remove strategy is first built to obtain the background training sets. Then, a DNN tensor decomposition-inspired convolutional AE is used to recover the original background information, which consists of an encoder, a low-rank tensor decomposition network, and a decoder. Finally, the residual errors between input HSI and recovered background are used for anomaly detection. Extensive experiments demonstrate the superiority of the TDNet in terms of both AUC values and ROC curves.