A composite amine absorbing solution which is an absorbing solution that absorbs CO 2 or H 2 S or both in a gas and is obtained by dissolving in water two kinds of linear monoamine (a) selected from a combination of a primary linear monoamine having a low steric hindrance and a primary linear monoamine having a high steric hindrance, a combination of a secondary linear monoamine, and a tertiary linear monoamine, a combination of a primary linear monoamine having a high steric hindrance and a secondary linear monoamine, and a combination of a primary linear monoamine having a high steric hindrance and a tertiary linear monoamine; a diamine (b), and an amide group-containing compound (d) having a boiling point at an atmospheric pressure of 130 °C or higher and having a dielectric constant at 25 °C of 20 or more, wherein a total concentration of the linear monoamine and the diamine is 40% to 60% by weight of the entire absorbing solution, a blending ratio ((the diamine (b) and the amide group-containing compound (d))/the linear monoamine (a)) of the diamine (b) and the amide group-containing compound (d) with respect to the linear monoamine (a) is 0.16 to 2.1, and when the two kinds of linear monoamine (a) are the primary linear monoamine having a low steric hindrance and the primary linear monoamine having a high steric hindrance, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the primary linear monoamine having a low steric hindrance) is set in a range / of 0.3 to 2.5, when the two kinds of linear monoamine (a) are the secondary linear monoamine and the tertiary linear monoamine, a weight ratio of (the tertiary linear monoamine)/(the secondary linear monoamine) is set in a range / of 0.3 to 2.5, when the two kinds of linear monoamine (a) are the primary linear monoamine having a high steric hindrance and the secondary linear monoamine, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the secondary linear monoamine) is set in a range / of 0.3 to 2.5, and when the two kinds of linear monoamine (a) are the primary linear monoamine having a high steric hindrance and the tertiary linear monoamine, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the tertiary linear monoamine) is set in a range / of 0.3 to 2.5. two kinds of linear monoamine (a) selected from a combination of a primary linear monoamine having a low steric hindrance and a primary linear monoamine having a high steric hindrance, a combination of a secondary linear monoamine, and a tertiary linear monoamine, a combination of a primary linear monoamine having a high steric hindrance and a secondary linear monoamine, and a combination of a primary linear monoamine having a high steric hindrance and a tertiary linear monoamine; a combination of a primary linear monoamine having a low steric hindrance and a primary linear monoamine having a high steric hindrance, a combination of a secondary linear monoamine, and a tertiary linear monoamine, a combination of a primary linear monoamine having a high steric hindrance and a secondary linear monoamine, and a combination of a primary linear monoamine having a high steric hindrance and a tertiary linear monoamine; a diamine (b), and an amide group-containing compound (d) having a boiling point at an atmospheric pressure of 130 °C or higher and having a dielectric constant at 25 °C of 20 or more, wherein a total concentration of the linear monoamine and the diamine is 40% to 60% by weight of the entire absorbing solution, a blending ratio ((the diamine (b) and the amide group-containing compound (d))/the linear monoamine (a)) of the diamine (b) and the amide group-containing compound (d) with respect to the linear monoamine (a) is 0.16 to 2.1, and when the two kinds of linear monoamine (a) are the primary linear monoamine having a low steric hindrance and the primary linear monoamine having a high steric hindrance, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the primary linear monoamine having a low steric hindrance) is set in a range / of 0.3 to 2.5, when the two kinds of linear monoamine (a) are the secondary linear monoamine and the tertiary linear monoamine, a weight ratio of (the tertiary linear monoamine)/(the secondary linear monoamine) is set in a range / of 0.3 to 2.5, when the two kinds of linear monoamine (a) are the primary linear monoamine having a high steric hindrance and the secondary linear monoamine, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the secondary linear monoamine) is set in a range / of 0.3 to 2.5, and when the two kinds of linear monoamine (a) are the primary linear monoamine having a high steric hindrance and the tertiary linear monoamine, a weight ratio of (the primary linear monoamine having a high steric hindrance)/(the tertiary linear monoamine) is set in a range / of 0.3 to 2.5.