Although substantial advances have been made in investigating the storage and transport properties of shale gas in past decades, understanding of the flow characteristics and gas-bearing property in organic pores remains limited. In this paper, organic pores in the organic matter (OM) of the marine Longmaxi Formation are classified into six types based on the morphology and sizes of nanoscale pores. The structures of the six types of typical organic pores under high temperature and pressure are investigated based on the digital core compressibility method introduced in this paper. The results show that the pore-size distribution and connectivity of organic pores under high temperature and pressure are considerably different from those under conventional conditions. The apparent permeability of OM with different proportions of macropores, mesopores, and micropores are analyzed. The results demonstrate that the permeability of OM with Type 1 organic pores has the largest changes after compaction, whereas OM with Type 5 organic pores has a relatively smaller change. The regularities of the absolute adsorption amount and the free gas amount of OM with typical organic pores are also investigated. The absolute adsorption amount of OM decreases with the proportion of macropores, whereas the amount of free gas of OM increases. Finally, a chart of the absolute adsorption amount and the free gas amount of OM at different depths is given, which is helpful for estimating the gas-bearing capacity of OM and preliminary understanding the quality of a shale reservoir.