Generalized　Pareto　distribution　(GPD),　an　asymmetrical　distribution,　primarily　models　exceedances　over　a　high　threshold　in　many　applications.　Within　the　peaks-over-threshold　(POT)　framework,　we　consider　a　new　GPD　parameter　estimation　method　to　estimate　a　common　tail　risk　measure,　the　value　at　risk　(VaR).　The　proposed　method　is　more　suitable　for　the　POT　framework　and　makes　full　use　of　data　information.　Specifically,　our　estimation　method　builds　upon　the　generalized　probability　weighted　moments　method　and　integrates　it　with　the　nonlinear　weighted　least　squares　method.　We　use　exceedances　for　the　GPD,　minimizing　the　sum　of　squared　differences　between　the　sample　and　population　moments　of　a　function　of　GPD　random　variables.　At　the　same　time,　the　proposed　estimator　uses　three　iterations　and　assigns　weight　to　further　improving　the　estimated　performance.　Under　Monte　Carlo　simulations　and　with　a　real　heavy-tailed　dataset,　the　simulation　results　show　the　advantage　of　the　newly　proposed　estimator,　particularly　when　VaRs　are　at　high　confidence　levels.　In　addition,　by　simulating　other　heavy-tailed　distributions,　our　method　still　exhibits　good　performance　in　estimating　misjudgment　distributions.