Suppression of secondary electron yield attracted much attention in areas such as accelerator and high power microwave components in recent years. To evaluate the suppression efficiencies of different surface topographies, the secondary electron yields (SEYs) of four kinds of micro-structured surfaces for trapping secondary electrons, i.e., triangular groove, rectangular groove, cuboid, cylindrical, are obtained by the phenomenological probabilistic model of secondary electron emission. The simulation results show that the SEYs of these structures are much dependent on the shape parameters such as aspect ratio or porosity. There are mainly three findings: 1) the SEY decreases with increasing aspect ratio and porosity; 2) the traps with cuboid or cylindrical shape are more efficient than triangular or rectangular traps for the SEY suppression; 3) the SEY dependence of micro-structured surface on incident angle is not as obvious as that of flat surface. Micro-trapping structure surfaces are fabricated by mechanical method, photolithography process and chemical etching respectively. The measured SEYs of these samples validate the theoretical results. All these results show that the proposed micro-structures as secondary electron traps have potential applications in SEY suppression in fields such as multipactor and electron-cloud effects.