A method of manufacturing an aluminum alloy wire, comprising: a rough drawing wire forming step of forming a rough drawing wire composed of an aluminum alloy, the aluminum alloy consisting of aluminum; the following additive elements: Si in an amount of 0.35 mass% to 0.75 mass%; Mg in an amount of 0.3 mass% to 0.7 mass%; optionally Cu in an amount of 0.4 mass% or less; optionally Fe in an amount of 0.6 mass% or less; optionally Ti and/or V, wherein the total content of Ti and V is 0.05 mass% or less; and unavoidable impurities; a rough drawing wire treatment step of obtaining an aluminum alloy wire by performing a treatment step on the rough drawing wire, wherein the treatment step includes at least one wire drawing treatment step; a first solution treatment step of forming a first solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 600 °C or less, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the first solution treatment step being performed immediately before the last wire drawing treatment step among the at least one wire drawing treatment step; a second solution treatment step of forming a second solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 650 °C or less for a heat treatment time of longer than 10 seconds to 3 hours, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the second solution treatment step being performed immediately after the last wire drawing treatment step; and an aging treatment step performed after the second solution treatment step by performing a heat treatment at 120°C to 300°C for 3 hours or more. a rough drawing wire forming step of forming a rough drawing wire composed of an aluminum alloy, the aluminum alloy consisting of aluminum; the following additive elements: Si in an amount of 0.35 mass% to 0.75 mass%; Mg in an amount of 0.3 mass% to 0.7 mass%; optionally Cu in an amount of 0.4 mass% or less; optionally Fe in an amount of 0.6 mass% or less; optionally Ti and/or V, wherein the total content of Ti and V is 0.05 mass% or less; and unavoidable impurities; a rough drawing wire treatment step of obtaining an aluminum alloy wire by performing a treatment step on the rough drawing wire, wherein the treatment step includes at least one wire drawing treatment step; a first solution treatment step of forming a first solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 600 °C or less, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the first solution treatment step being performed immediately before the last wire drawing treatment step among the at least one wire drawing treatment step; a second solution treatment step of forming a second solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 650 °C or less for a heat treatment time of longer than 10 seconds to 3 hours, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the second solution treatment step being performed immediately after the last wire drawing treatment step; and an aging treatment step performed after the second solution treatment step by performing a heat treatment at 120°C to 300°C for 3 hours or more. Si in an amount of 0.35 mass% to 0.75 mass%; Mg in an amount of 0.3 mass% to 0.7 mass%; optionally Cu in an amount of 0.4 mass% or less; optionally Fe in an amount of 0.6 mass% or less; optionally Ti and/or V, wherein the total content of Ti and V is 0.05 mass% or less; and unavoidable impurities; a rough drawing wire treatment step of obtaining an aluminum alloy wire by performing a treatment step on the rough drawing wire, wherein the treatment step includes at least one wire drawing treatment step; a first solution treatment step of forming a first solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 600 °C or less, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the first solution treatment step being performed immediately before the last wire drawing treatment step among the at least one wire drawing treatment step; a second solution treatment step of forming a second solution treatment material by forming a solid solution of the aluminum and the additive element by heating the wire material at a heat treatment temperature of 450°C or more and 650 °C or less for a heat treatment time of longer than 10 seconds to 3 hours, and then performing a quenching treatment by cooling at a cooling rate of 100 K/min or more, the second solution treatment step being performed immediately after the last wire drawing treatment step; and an aging treatment step performed after the second solution treatment step by performing a heat treatment at 120°C to 300°C for 3 hours or more.