The local oxidation using an atomic force microscopy (AFM) is useful for Si-based fabrication of nanoscale structures and devices. SiC is a wide band-gap material that has advantages such as high-power, high-temperature and high-frequency in applications, and among several SiC polytypes, 4H-SiC is the most attractive polytype due to the high electron mobility. However, the AFM local oxidation of 4H-SiC for fabrication is still difficult, mainly due to the physical hardness and chemical inactivity of SiC. In this paper, we investigated the local oxidation of 4H-SiC surface using an AFM. We fabricated oxide patterns using a contact mode AFM with a Pt/Ir-coated Si tip (N-type, 0.01-0.025 ${Omega}cm$) at room temperature, and the relative humidity ranged from 40 to 50 %. The height of the fabricated oxide pattern (1-3 nm) on SiC is similar to that of typically obtained on Si ($10^{15}^{sim}10^{17}$ $cm^{-3}$). We perform the 2-D simulation to further analyze the electric field between the tip and the surface. We demonstrated that a specific electric field (4 ${ imes}$ $10^7;V/m$) and a doping concentration ($^{sim}10^{17}$ $cm^{-3}$) is sufficient to switch on/off the growth of the local oxide on SiC.