The fluorescence extended X-ray absorption fine structures near the Ba-L(3) edge of a Ba-arachidate (CH3(CH2)(18)COO2Ba) Langmuir-Blodgett film are investigated by using polarized X-rays from a synchrotron radiation source. From the analysis of the observed spectra for different incident angles, the absorption-site geometries are obtained. The distance from the Ba ion to the nearest neighbor oxygen atoms, lying almost in the Ba plane, is found to be 0.278 nm. Taking account of the reported structural data, a local structure model around the Ba ion is proposed.