Industrial pumps are essential components in various sectors, such as manufacturing, energy production, and water treatment, where their failures can cause significant financial and safety risks. Anomaly detection can be used to reduce those risks and increase reliability. In this work, we propose a novel enhanced convolutional neural network (ECNN) to predict the failure of an industrial pump based on the vibration data captured by an acceleration sensor. The convolutional neural network (CNN) is designed with a focus on low complexity to enable its implementation on edge devices with limited computational resources. Therefore, a detailed design space exploration is performed to find a topology satisfying the trade-off between complexity and accuracy. Moreover, to allow for adaptation to unknown pumps, our algorithm features a pump-specific parameter that can be determined by a small set of normal data samples. Finally, we combine the ECNN with a threshold approach to further increase the performance and satisfy the application requirements. As a result, our combined approach significantly outperforms a traditional statistical approach and a classical CNN in terms of accuracy. To summarize, this work provides a novel, low-complex, CNN-based algorithm that is enhanced by classical methods to offer high accuracy for anomaly detection of industrial pumps.