Abstract: Based on the nucleon-pair shell model truncated to an SD collective pair subspace, the low-lying spectra, wave function structures of the eigenstates and electromagnetic (EM) transition strengths of the Barium isotopes (^{130,132,134,136}Ba) are studied systematically. The SDI method and TDA approximation method are adopted to construct the SD pairs. It is shown that they have their advantages and disadvantages, and there is no absolute dominant solution between them for studying Barium isotopes. The results of two methods are both close to the experiment values. It is found that the larger the number of the neutron hole pairs, the better the agreement between the experiments and the calculations. They can all find the results of the internal relationship between the EM transition strengths and the structure for the wave function. In the description of the low-lying spectra for the Barium isotopes, the calculations of the yrast band and the quasi-γ band calculated by SDI method are better generally. But the first 3⁺ states are higher than the experiments and the second 0⁺ states are lower than the experiments by SDI method. These disadvantages are improved by TDA approximation method. In the description of EM transition strengths of the Barium isotopes, the calculations are better by TDA approximation method which considering multibody effects. Sometimes, the results given by the SDI method could be even better than those calculated with the TDA approximation method by selecting the appropriate interaction strengths.