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Anomalous audio in speech recordings is often caused by speaker voice distortion, external noise, or even electric interferences. These obstacles have become a serious problem in some fields, such as high-quality music mixing and speech processing. In this paper, a novel approach using a temporal convolutional attention network (TCAN) is proposed to tackle this problem. The use of temporal conventional network (TCN) can capture long range patterns using a hierarchy of temporal convolutional filters. To enhance the ability to tackle audio anomalies in different acoustic conditions, an attention mechanism is used in TCN, where a self-attention block is added after each temporal convolutional layer. This aims to highlight the target related features and mitigate the interferences from irrelevant information. To evaluate the performance of the proposed model, audio recordings are collected from the TIMIT dataset, and are then changed by adding five different types of audio distortions: gaussian noise, magnitude drift, random dropout, reduction of temporal resolution, and time warping. Distortions are mixed at different signal-to-noise ratios (SNRs) (5dB, 10dB, 15dB, 20dB, 25dB, 30dB). The experimental results show that the use of proposed model can yield better classification performances than some strong baseline methods, such as the LSTM and TCN based models, by approximate 3$\sim$ 10\% relative improvements.