Destructive methods were used for the burnup determination of U-Zr alloy nuclear fuel irradiated in the High-flux Advanced Neutron Application Reactor (HANARO) at KAERI. The dissolution rate of unirradiated U-Zr alloy fuel in $HNO_3$/HF mixtures was investigated for the experimental conditions of a different temperature, and initial concentrations of HF and $HNO_3$. The irradiated U-Zr alloy fuel specimen was dissolved in a mixed acid condition of 3 M HNO3 and 1 M HF at $90^{circ}C$ for 8 hours under reflux. The total burnup was determined from measurement of the Nd isotope burnup monitors. The method includes U, Pu, $^{148}Nd,;^P{145}Nd+^{146}Nd,;^{144}Nd+^{143}Nd$ and total Nd isotopes determination by the isotope dilution mass spectrometric method (IDMS) using triple spikes $(^{233}U,;^{242}Pu;and;^{150}Nd)$. The effective fission yield was calculated from the weighted fission yields averaged over the irradiation period. The results are compared with that obtained by the destructive -spectrometric measurement of the $^{137}Cs$ monitor.