A method for manufacturing a copper alloy tube with excellent high-temperature brazeability, the method comprising: a solutionizing step (S11) of heating and holding a tubular extrusion material, made from a chromium-zirconium-copper alloy having a composition consisting of 0.5 to 1.5 mass% Cr, 0.02 to 0.20 mass% Zr, and the remaining components being unavoidable impurities and Cu, at a solutionizing temperature of 900°C or greater, and then water-quenching the tubular extrusion material; thereafter, a main process step (S21) comprising a set of steps including a drawing process step (S12) of drawing the tubular extrusion material to obtain a drawn material, and an intermediate annealing step (S13) of heating at an annealing temperature and then water-quenching the drawn material; and an adjusting process step (S14) of further drawing the drawn material and setting average crystal grain sizes in a vertical cross section (A1) along an axis as well as a horizontal cross section (A2) orthogonal to the axis to 50 micrometers or less each; the average crystal grain sizes of the vertical cross section (A1) and the horizontal cross section (A2) each being set to 100 micrometers or greater and the annealing temperature being set to 900°C or greater after the solutionizing step, thereby making the average crystal grain sizes of the vertical cross section and the horizontal cross section 100 micrometers or less after the adjusting process step, and after heating is performed at 980°C for 30 minutes followed by air-cooling; wherein the adjusting process step (S14) performs the drawing process (S12) at a surface area reduction rate of 40% or greater of the horizontal cross section (A2). a solutionizing step (S11) of heating and holding a tubular extrusion material, made from a chromium-zirconium-copper alloy having a composition consisting of 0.5 to 1.5 mass% Cr, 0.02 to 0.20 mass% Zr, and the remaining components being unavoidable impurities and Cu, at a solutionizing temperature of 900°C or greater, and then water-quenching the tubular extrusion material; thereafter, a main process step (S21) comprising a set of steps including a drawing process step (S12) of drawing the tubular extrusion material to obtain a drawn material, and an intermediate annealing step (S13) of heating at an annealing temperature and then water-quenching the drawn material; and an adjusting process step (S14) of further drawing the drawn material and setting average crystal grain sizes in a vertical cross section (A1) along an axis as well as a horizontal cross section (A2) orthogonal to the axis to 50 micrometers or less each; the average crystal grain sizes of the vertical cross section (A1) and the horizontal cross section (A2) each being set to 100 micrometers or greater and the annealing temperature being set to 900°C or greater after the solutionizing step, thereby making the average crystal grain sizes of the vertical cross section and the horizontal cross section 100 micrometers or less after the adjusting process step, and after heating is performed at 980°C for 30 minutes followed by air-cooling; wherein the adjusting process step (S14) performs the drawing process (S12) at a surface area reduction rate of 40% or greater of the horizontal cross section (A2). <EOS>