The invention discloses a method for rapidly recovering rhenium, copper and lead from copper smelting waste acid and a device for implementing the method. According to the method, the copper smelting waste acid is subjected to lead removing through filtering, lead residues with the lead content higher than 55% are obtained and taken as lead extraction raw materials, the lead extraction raw materials are subjected to targeted rhenium precipitation, rhenium-rich residues are obtained and are subjected to hot-pressing oxidizing leaching, a rhenium-rich leaching agent is obtained, the rhenium-rich leaching agent after evaporation and concentration is subjected to KCl rhenium precipitation and recrystallization, potassium perrhenate is prepared, and a liquid obtained after rhenium precipitation is vulcanized for copper deposition. The device comprises a rhenium and copper precipitant storage tank, a precipitation tank, a flocculating agent storage tank, a flocculation reaction tank, a reaction kettle, an evaporation-crystallization device, a centrifugal separator, a waste acid anti-gravity-osmosis filter, a rhenium-rich copper residue anti-gravity-osmosis filter, a filter press, a rhenium and copper precipitation tank steam heating system, a copper precipitation tank steam heating system and a slurry pump. The method and the device have the characteristics of low investment, rapid and short procedures, simple and efficient operation, and high recovery rate, and are clean and environment-friendly.