Topological　base　plays　a　foundational　role　in　topology　theory.　However,　few　works　have　been　done　to　find　the　minimal　base,　which　would　make　us　difficult　to　interpret　the　internal　structure　of　topological　spaces.　To　address　this　issue,　we　provide　a　method　to　convert　the　finite　topological　space　into　Boolean　matrix　and　some　properties　of　minimal　base　are　investigated.　According　to　the　properties,　an　algorithm(URMB)　is　proposed.　Subsequently,　the　relationship　between　topological　space　and　its　sub-space　with　respect　to　the　base　is　concentrated　on　by　Boolean　matrix.　Then,　a　fast　algorithm(MMB)　is　presented,　which　can　avoid　a　mass　of　redundant　computations.　Finally,　some　numerical　experiments　are　given　to　show　the　advantage　and　the　effectiveness　of　MMB　compared　with　URMB.