The contents of transuranic elements in high-burnup spent fuel samples were determined. The activity amounts of $^{238}Pu,;^{239}Pu,;^{240}Pu,;^{241}Am,;^{244}Cm;and;^{242}Cm$ were measured by alpha spectrometry using $^{242}Pu;and;^{243}Am$ as tracers, respectively. A spike addition method for $^{237}Np$ was established by an alpha and gamma spectrometry using $^{239}Np$ as a spike after the optimum conditions for the measurements of $^{237}Np;and;^{239}Np$, respectively, were obtained. A separation system using anion exchange chromatography and diethylhexylphosphoric acid extraction chromatography was applied for the separation of these elements. This method was applied to high-burnup spent nuclear fuel samples $(40{sim}60GWD/MTU)$. The contents of the transuranic elements were compared with those by ORIGEN-2 code. Measurements and the calculations of the contents of the plutonium isotopes $^{238}Pu,;^{239}Pu;and;^{240}Pu$ agreed to within 10% on average. The contents of $^{237}Np$ agreed to within approximately 5% except for one instance of a calculation, while those of $^{241}Am,;^{244}Cm;and;^{242}Cm$ showed higher values by approximately 19%, 35% and 14% on average, respectively, compared to the calculations according to the burnup.