As a novel quantum state, Majorana zero mode (MZM) has become a hot topic due to its applications in topological quantum computing. Theories predict that MZM can appear in the vortex core of a topological superconductor as a unique bound state. However, due to the existence of trivial low-energy vortex states or impurity states, it is usually difficult to identify MZM and study their physical properties. In this talk, I will introduce our recent high resolution STM studies on vortex state of FeSe based High-Tc superconductors. We found clear zero-energy mode which well separated from other high-level vortex state in the intercalated (Li, Fe)OHFeSe. Its non-trivial nature is supported by evidence of quantized conductance, and the distinct spatial distribution with comparing to other high-energy level states. As for single-layer FeSe/SrTiO3 film, it only displays conventional Caroli-de Gennes- Matricon (CdGM) states without zero-energy mode. These results provide critical information on the fast-developing field of topological superconductivity and MZM.