Nowadays, Anomaly Detection (AD) in time series plays important roles in many fields, such as industrial production, finance, network security and medical health. Recently, the advancement of Internet of Things (IoT) has led to the emergence of intelligent manufacturing and the widespread usage of edge devices. As a result, there is an increasing demand for rapid and effective anomaly detection in the time series data captured at the edge. However, it is still challenging to design an efficient and effective time series anomaly detection approach, which is suitable for edge environments, due to real-time constraints and limited resources. To address this issue, we propose a novel anomaly detection neural network, namely, Efficient Periodicity-Aware Anomaly Detection Network (EPAAD- Net). This network is mainly designed on top of one-dimensional convolutions, which ensure low inference latency for edge deployment. We also deliberately design a Sine-Cosine Transform Module (SCTM), which projects the extracted features onto periodic basis functions to introduce a periodic inductive bias, thereby boosting the performance of the network. To capture the long-term dependencies between data points, we further incorporate a cross-attention module into the EPAAD- Net. Experimental results demonstrate that the proposed EPAAD-Net achieves competitive detection accuracy compared to 14 baselines across six data sets, while offering higher inference efficiency. We believe that these promising results should be due to the joint use of the simple network architecture and the periodicity-aware SCTM.