A flux-free brazing aluminum alloy brazing sheet includes: a core material formed of aluminum alloy comprising Si of 0.50 to 0.90 mass %, Cu of 0.30 to 2.50 mass %, and Mn of 1.40 to 1.80 mass %, with a Mg content limited to 0.05 mass % or less, and with the balance being Al and inevitable impurities; an intermediate material being formed of aluminum alloy comprising Mg of 0.40 to 1.00 mass %, and Zn of 2.00 to 6.00 mass %, with the balance being Al and inevitable impurities; and a brazing material being formed of aluminum alloy comprising Si of 6.00 to 13.00 mass %, Mg of 0.05 to 0.40 mass %, and Bi of 0.010 to 0.050 mass %, with the balance being Al and inevitable impurities.