This paper shows the design and evaluation of an FPGA-based accelerator for sliding-window aggregation over data streams with out-of-order data arrival. We propose an order-agnostic hardware implementation technique for windowing operators based on a one-pass query evaluation strategy called Window-ID, which is originally proposed for software implementation. The proposed implementation succeeds to process out-of-order data items, or tuples, at wire speed due to the simultaneous evaluations of overlapping sliding-windows. In order to verify the effectiveness of the proposed approach, we have also implemented an experimental system as a case study. Our experiments demonstrate that the proposed accelerator with a network interface achieves an effective throughput around 760 Mbps or equivalently nearly 6 million tuples per second, by fully utilizing the available bandwidth of the network interface.