Autoencoder, a neural-network based dimensionality reduction algorithm has demonstrated its effectiveness in anomaly detection. It can detect whether an input sample is normal or abnormal by just training only with normal data. In general, Autoencoder is built on backpropagation-based neural networks (BP-NNs). When BP-NNs are implemented in edge devices, they are typically specialized only for prediction with weight matrices precomputed offline due to the high computational cost. However, such devices cannot be immediately adapted to time-series trend changes of input data. In this paper, we propose an FPGA-based unsupervised anomaly detector, called OS-ELM-FPGA, that combines Autoencoder and an online sequential learning algorithm OS-ELM. Based on our theoretical analysis of the algorithm, the proposed OS-ELM-FPGA completely eliminates matrix pseudoinversions while improving the learning throughput. Simulation results using open-source datasets show that OS-ELM-FPGA achieves favorable anomaly detection accuracy compared to CPU and GPU implementations of BP-NNs. Learning throughput of OS-ELM-FPGA is 3.47x to 27.99x and 5.22x to 78.06x higher than those of CPU and GPU implementations of OS-ELM. It is also 3.62x to 36.15x and 1.53x to 43.44x higher than those of CPU and GPU implementations of BP-NNs.