Coumarin and their derivatives have drawn much attention in the pharmacological and pharmaceutical fields due to their broad range and diverse biological activities. In the present work, starting from the 6-amino-7-hydroxy-4-methyl-2H-chromen-2-one, a series of 6-(substituted benzylamino)-7-hydroxy-4-methyl-2H-chromen-2-ones 1–11 was synthesized and assessed for their anti-inflammatory activity using the carrageenan-induced hind paw edema method. Compounds 2, 3, 4 and 9 showed significant (p < 0.001) reduction of rat paw edema volume after 1 h from the administration of the carrageenan compared to the reference drug, indomethacin. On the other hand, compounds 4 and 8 showed the highest anti-inflammatory activity, surpassing indomethacin after 3 h with 44.05% and 38.10% inhibition, respectively. Additionally, a molecular docking study was performed against the COX enzyme using the MOE 10.2010 software.