The positron implantation profiles and depth distribution in metal, semiconductor, and polymer surfaces are simulated using the Monte-Carlo-method-based Geant4 toolkit. As per the slow positron beam technique, the monoenergetic positron beams (in the range from 1 to 35 keV) with 1.5 mm radius is injected into semi-infinite samples in the present work. The implantation profile of 3.1 keV positrons in Fe is in good agreement with the Makhovian profile. The mean depth and depth resolution exhibit a general negative correlation with the material densities and incident position energy, respectively, while the fixed peak energy of backscattered positrons exhibits a net correlation with atomic number Z. Furthermore, the implantation profiles present better z-axis resolution with increasing incident angle, and this effect is more prominent for low-density materials. The results can provide theoretical support for new measurement methods based on the slow positron beam technique, such as segment measurements and micro-beam scanning measurements.