Using global magnetohydrodynamic simulations, we construct a 3D parametric model of the Martian magnetic pileup boundary (MPB). This model employs a modified parabola function defined by four parameters. The effects of the solar wind dynamic pressure, the solar wind densities and velocities, and the intensity and orientation of the interplanetary magnetic field (IMF) are examined using 267 simulation cases. The results from our parametric model show that (1) the MPB moves closer to Mars when the upstream solar wind dynamic pressure (Pd) increases, the subsolar standoff distance decreases and the flaring degree of the Martian MPB increases with an increasing Pd according to the power-law relations. For the same Pd, a higher solar wind velocity (a lower density) leads to a farther location of the MPB from Mars, along with a larger flaring degree, which is explained by the higher solar wind convection electric fields and a stronger magnetic pileup process under these conditions. (2) Larger Y or Z components of the IMF, BY or BZ, result in a thicker pileup region and a farther MPB location from Mars, as well as a decrease in the flaring degree. The radial IMF component, BX, has little effect on the geometry of the MPB. (3) In most of the simulations used to derive the current parametric model, the strongest Martian crustal magnetic field is located on the dayside. However, for a larger value of the southward IMF, the Martian MPB is located farther away in the northern hemisphere instead of the southern hemisphere. The north-south asymmetry of the Martian MPB with the southern hemisphere being farther away is observed for other IMF directions. We suggest that the magnetic reconnection of the southward IMF with the crustal field that occurs at middle latitudes of the southern hemisphere results in different magnetic field topologies and the closer location of the MPB under these conditions. Our model results show a relatively good agreement with the previous empirical and theoretical models.