The invention discloses a hot extrusion device for molybdenum and molybdenum alloy. The hot extrusion device comprises an extrusion die, the extrusion die is internally provided with an extrusion channel, and the middle of the extrusion channel retracts; the extrusion die is sleeved with a heat-preservation preheating device; the hot extrusion device further comprises a vertical hydraulic press and a pair of overturn extrusion devices, the overturn extrusion devices are used for turning over and laterally extruding the extrusion die, and the vertical hydraulic press is used for longitudinallyextruding and heating the molybdenum or molybdenum alloy in the extrusion channel. The invention further discloses a hot extrusion method for the molybdenum and molybdenum alloy. The method comprisesthe steps of preheating of the extrusion die, die combination and preheating, extrusion molding and 2-5 times of repeated extrusion molding. The hot extrusion device can unevenly extrude the molybdenum and molybdenum alloy in three phases, and large-sized even grain-refined molybdenum and molybdenum alloy are obtained; by means of the hot extrusion method, obtained finished materials of molybdenumand molybdenum alloy can be even in structure and refinement degree.