Example 1: To a stainless steel reactor equipped with a thermocouple, a stirrer, a gas supply line and a liquid supply line, 5.40 g (0.016 mol) of octacarbonyldicobalt(0) [Co2(CO)8] and 39.86 g of 1,4-dioxane (38.7 wt% of the total 1,4-dioxane) were added and stirred. Subsequently, a mixture of carbon monoxide and hydrogen [CO/H2 = 2.3/1 (molar ratio)] was introduced into the reactor to bring the pressure in the reactor to 13 MPa (gauge pressure). The temperature of the reactor was increased to 68-72 °C while maintaining stirring, at which time the pressure in the reactor was maintained at 13 MPa (gauge pressure). Next, 31.57 g (0.30 mol) of 3-(methylthio)propionaldehyde [compound shown in formula (2), wherein R1 is 2-methylthioethyl], 18.08 g (0.30 mol) of acetamide [compound shown in formula (3), wherein R2 is a methyl group and R3 is a hydrogen atom], 63.14 g of 1 ,4-dioxane (as a proportion of the total amount of 1,4-dioxane 61.3 wt%) and 5.40 g of water in a mixed solution with a titration time of 1.5 hours. After the dropwise addition, the reaction was continued with stirring at 68-72 °C for 4 h. Subsequent cooling to 5-35 °C gave 158.3 g of 1,4-dioxane solution containing N-acetyl-L-methionine. The yield of N-acetyl-L-methionine in this solution was analyzed by liquid chromatography to be 85.5% relative to 3-(methylthio)propionaldehyde.