The Lyapunov stability theory-based adaptive filter (LST-AF) is a robust filtering algorithm which the tracking error quickly converges to zero asymptotically. Recently, the software module of the LST-AF algorithm is effectively used in engineering applications such as tracking, prediction, noise cancellation and system identification problems. Therefore, hardware implementation becomes necessary in many cases where real time procedure is needed. In this paper, an implementation of the LST-AF algorithm on Field Programmable Gate Arrays (FPGA) is realized for the first time to our knowledge. The proposed hardware implementation on FPGA is performed for two main benchmark problems; i) tracking of an artificial signal and a Henon chaotic signal, ii) estimation of filter parameters using a system identification model. Experimental results are comparatively presented to test accuracy, performance and logic occupation. The results show that our proposed hardware implementation not only conserves the capabilities of software versions of the LST-AF algorithm but also achieves a better performance than them.