The invention discloses a self-sealing square hose and circular hose conversion joint resistant to the medium-high pressure and sealing and connecting methods for hoses, and relates to the technical filed of sealing and connection of hoses. The conversion joint comprises a body, a sleeve provided with a conical table at one end, a pressing sleeve provided with a conical hole in one end, and a pressing block, wherein a rectangular hole is formed in the pressing block; and a connecting block is fixedly arranged at one end of the joint body, a mounting blind hole is formed in the joint body, thepressing block can be compressed towards the joint body, the sleeve and the pressing sleeve are arranged in the mounting blind hole, and the pressing sleeve can be compressed towards the sleeve. The sealing and connecting method for the circular hose refers to the sleeve and the pressing sleeve, the hose penetrates through the pressing sleeve and is inserted into the sleeve, the pressing sleeve ismoved to enable the conical table to extrude the hose, and thus sealing and connecting is completed; the sealing and connecting method for the square hose refers to the connecting block and the pressing block, the hose penetrates through the pressing block and is connected to the connecting block in a sleeving mode, the pressing block is moved to enable the hose to be connected and sealed under extruding of the connecting block and the pressing block. According to the sealing and connecting methods, connecting is reliable, a sealing piece does not need to be additionally arranged, and the cost is low; and the conversion joint is simple in structure and convenient and quick in operation, and can bear the medium-high pressure load.