An acid gas recovery method, comprising: bringing target gas containing acid gas into gas-liquid contact with an absorbent amine solution to cause the absorbent amine solution to absorb the acid gas and remove the acid gas from the target gas; releasing the acid gas from the absorbent amine solution that has absorbed the acid gas, thereby regenerating the absorbent amine solution; causing chelate resin to adsorb iron ions in the absorbent amine solution by causing the absorbent amine solution to pass through the chelate resin; causing a regenerant solution to pass through the chelate resin having iron ions adsorbed thereon, thereby desorbing the iron ions to regenerate the chelate resin and obtain the regenerant solution containing the iron ions; quantitatively measuring the iron ions in the regenerant solution containing the iron ions and calculating the concentration of iron ions in the absorbent amine solution; and using a controller which includes a function to calculate the concentration of iron ions in the absorbent amine solution from a flow rate of a sample of the absorbent amine solution having passed through a quantitative measurement sample preparing device, a flow rate of the regenerant solution discharged from the quantitative measurement sample preparing device, and a value of an absorbance measured by an absorptiometer for the regenerant solution containing iron ions, using the calibration curve of the concentration of iron ions, wherein, when the calculated concentration of iron ions in the absorbent amine solution is not less than a threshold set in a range from 1 to 10 ppm, the controller instructs a reclaiming device for removing iron ions to activate in order to remove iron ions in the absorbent amine solution, wherein, when the reclaiming device is activated by the controller, a part of the absorbent amine solution is introduced into the reclaiming device from a line (L 81) and is heated by an evaporator to a temperature at which the amine compound is vaporized, wherein the vaporized amine compound is condensed with a cooler to be regenerated as the absorbent amine solution, which is then returned from a line (L 83) to a line (L 8) from a lean solution to be reused, and wherein the iron ions and oxidized degraded substances of the amine compound which remain without being evaporated are discharged from a line (L 82) as sludge. bringing target gas containing acid gas into gas-liquid contact with an absorbent amine solution to cause the absorbent amine solution to absorb the acid gas and remove the acid gas from the target gas; releasing the acid gas from the absorbent amine solution that has absorbed the acid gas, thereby regenerating the absorbent amine solution; causing chelate resin to adsorb iron ions in the absorbent amine solution by causing the absorbent amine solution to pass through the chelate resin; causing a regenerant solution to pass through the chelate resin having iron ions adsorbed thereon, thereby desorbing the iron ions to regenerate the chelate resin and obtain the regenerant solution containing the iron ions; quantitatively measuring the iron ions in the regenerant solution containing the iron ions and calculating the concentration of iron ions in the absorbent amine solution; and using a controller which includes a function to calculate the concentration of iron ions in the absorbent amine solution from a flow rate of a sample of the absorbent amine solution having passed through a quantitative measurement sample preparing device, a flow rate of the regenerant solution discharged from the quantitative measurement sample preparing device, and a value of an absorbance measured by an absorptiometer for the regenerant solution containing iron ions, using the calibration curve of the concentration of iron ions, wherein, when the calculated concentration of iron ions in the absorbent amine solution is not less than a threshold set in a range from 1 to 10 ppm, the controller instructs a reclaiming device for removing iron ions to activate in order to remove iron ions in the absorbent amine solution, wherein, when the reclaiming device is activated by the controller, a part of the absorbent amine solution is introduced into the reclaiming device from a line (L 81) and is heated by an evaporator to a temperature at which the amine compound is vaporized, wherein the vaporized amine compound is condensed with a cooler to be regenerated as the absorbent amine solution, which is then returned from a line (L 83) to a line (L 8) from a lean solution to be reused, and wherein the iron ions and oxidized degraded substances of the amine compound which remain without being evaporated are discharged from a line (L 82) as sludge.