The present invention discloses a method for manufacturing a tube of copper or copper alloy (1), including: a) removing a surface oxidation layer from a tubular blank; b) rapidly rolling said tubular blank by means of a four-planet rolling mill (2, 6, 7) ; c) rapidly cooling down said tubular blank; d) linearly drawing the cooled-down tubular blank with a linear drawing equipment. In said manufacturing method, a four-planet rolling mill with a relatively strong strength is utilized. It provides a faster rolling speed, which is about three times of that in the prior art . Consequently, huge deformation heat is produced. A two-stage cooling down is subsequently carried out so that the recrystallization process of the coarse casting structures may be accelerated. The grains after recrystallization are small and uniform, with sizes of 0.010-0.040mm. Meanwhile, the drawing process for the tubular blank may reduce the defects on the tubular surface.