An object of the present invention are to provide a protease that is stable in a wide pH range from acidic to alkaline, and that has excellent thrombolytic activity; a protease-producing microorganism that produces the above protease; and a process for producing the protease. By culturing a novel filamentous fungus belonging to the genus Fusarium (Fusarium sp. strain BLB), a protease that is stable in a wide pH range from acidic to alkaline and that has excellent thrombolytic activity, is formed and accumulated in the culture medium, and recovered.