Using global MHD simulations, we construct a 3D parametric Martian bow shock model that employs a generalized conic section function defined by seven parameters. Effects of the solar wind dynamic pressure (Pd), the magnetosonic Mach number (MMS), and the intensity and the orientation of the interplanetary magnetic field (IMF) on the seven parameters are examined based on 250 simulation cases. These 250 cases have a Pd range of 0.36-9.0nPa (the solar wind number density varying from 3.5 to 12/cm^3^ and the solar wind speed varying from 250 to 670km/s), an MMS range of 2.8-7.9, and an IMF strength range from zero to 10nT. The results from our parametric model show several things. (1) The size of the Martian bow shock is dominated by Pd. When Pd increases, the bow shock moves closer to Mars, and the flaring of the bow shock decreases. (2) The MMS has a similar effect on the bow shock as Pd but with different coefficients. (3) The effects of IMF components on the bow shock position are associated with the draping and pileup of the IMF around the Martian ionosphere; hence, we find that both the subsolar standoff distance and the flaring angle of the bow shock increase with the field strength of the IMF components that are perpendicular to the solar wind flow direction (BY and BZ in the MSO coordinate system). The parallel IMF component (BX) has little effect on the subsolar standoff distance but affects the flaring angle. (4) The cross section of the bow shock is elongated in the direction perpendicular to the IMF on the Y-Z plane, and the elongation degree is enhanced with increasing intensities of BY and BZ. The north-south (dawn- dusk) asymmetry is controlled by the cone angle when the IMF is on the X-Z (X-Y) plane. These results show a good agreement with the previous empirical and theoretical models. The current parametric model is obtained under solar maximum conditions with the strongest Martian crustal magnetic field located at the subsolar point. In fact, the bow shock shape can also be affected by both the solar extreme ultraviolet radiation and the orientation of crustal magnetic anomalies to the Sun, which should be considered in future models.