The present-day Martian crust is likely to be dominated by the basaltic secondary crust formed via the extrusion of basaltic magma from the partially molten Martian mantle. However, it is still unknown if the Mars possessed other crustal types. In this work, we investigate the growth of the Martian crust using the 1-D parameterized mantle convection model. In order to account for the crustal thickness, crustal Th abundance and mantle potential temperature at the present-day, a silica-rich primitive crust thicker than 6-10 km must be formed before 4.5 Ga. During consequential evolution, the primitive crust of the northern hemisphere would be destroyed by the Borealis impact at ∼ 4.48 Ga, but the primitive crust of the southern hemisphere still survives and is buried below the ejecta of the Borealis impact and the basaltic secondary crust. Besides, the water content of the Martian mantle depends strongly on the predominant creep style therein. The dominance of diffusion creep corresponds to a Martian mantle drier than the terrestrial mantle, whereas the dominance of dislocation creep in the Martian mantle may allow an Earth-like water content in the Martian mantle.