Pseudo-cubic tetragonal boron, which may be another form of boron allotropes, has recently been discovered under high pressure and high temperature conditions. In this paper, the structure of pseudo-cubic tetragonal boron is studied by density-functional-theory (DFT) calculation. The structure is abnormal compared with other boron allotropes in many respects, making it difficult to comprehend. The lattice is very close to a cubic lattice, such that the icosahedra are largely distorted along the c-axis. Such distortions are normally not favorable for boron crystals; in fact, the present calculations supported this. The reported positions of partially occupied interstitial sites render the intericosahedral bonds unusually long or short, which were again not supported by the present calculations. Furthermore, the potential of involving impurities is unlikely in terms of the formation energy and lattice parameters. Therefore, the structure of pseudo-cubic tetragonal boron was not proven by calculation, despite this extensive study. Something may be overlooked in the present structural model, or something unusual may have happened in this structure, the solution of which is left as an open question.