Context. The draping of the interplanetary magnetic field (IMF) around unmagnetized planets induces a magnetotail with a two-lobe plasma structure. On Mars, due to the impact of the IMF Parker spiral angle, the structure of its induced magnetotail is dawn-dusk asymmetric. Observational and numerical studies have shown the dawn-dusk asymmetric size of magnetic lobes and the shift of the polarity reversal layer and the inverse polarity reversal layer under different Parker spiral angles. Variation in the tail-region induced magnetic field with the Parker spiral angle is important in the evolution of the magnetotail. Further studies should investigate the influence of the magnetic pressure and field direction on the magnetic lobe structure and plasma boundary locations, as well as the relationship between the polarity reverse of the IMF and the Parker spiral angle. Aims. This study aims to investigate the dawn-dusk asymmetric structure of the Martian magnetotail under different Parker-spiral IMF orientations. In this study, we used a multispecies magnetohydro-dynamic (MHD) model, which has been shown to self-consistently calculate the Mars-solar wind interaction, to investigate the effects of the Parker spiral angle on the structure of the Martian magnetotail. By comparing the magnetic field, large-scale configurations, and plasma boundary locations across various cases, we aim to clarify how variations in the IMF Parker spiral angle affect the magnetic pressure and field direction in the magnetotail and the locations and shapes of the magnetic lobes, polarity reversal layer, and inverse polarity reversal layer. Methods. A three-dimensional and parallelized multispecies MHD model was constructed to simulate the global solar wind interaction with Mars. Four ion species, H+, O2+, O+, and CO2+, as well as the chemical reactions between them, such as photoionization, charge exchange, and recombination, were considered in the model to accurately calculate the ion distributions in the magnetosphere and ionosphere of Mars. Three cases with Parker spiral angles of 90, 56, and 30 degrees were examined, representing the perpendicular, standard, and quasi-parallel IMF relative to the solar wind flow, respectively. Results. A symmetric magnetotail was reproduced in the case with a Parker spiral angle of 90° degrees. When the Parker spiral angle decreases, the magnetic pressure in the magnetic lobes reduces, and the flaring angle of the magnetic field becomes larger on the dawn side than on the dusk side. These two factors result in the shrinkage and extension of the magnetic lobes. Furthermore, the variation in magnetic pressure results in a polarity reversal layer bent toward the dawn side. Finally, we found that the inverse polarity reversal layer shrinks toward Mars with a decrease in the Parker spiral angle.