A new series of 4H-chromene-3-carboxylate derivatives were synthesized using multicomponent reaction of salicylaldehyde, ethyl acetoacetate and dimedone in ethanol with K3PO4 as a catalyst at 80 °C. The structures of all newly synthesized compounds were confirmed by spectral techniques viz. IR, 1H NMR, 13C NMR, and LCMS analysis. The newly synthesized compounds 4a to 4j were screened against elastase enzyme. Interestingly, all these compounds found to be potent elastase inhibitors with much lower IC50 value. The compound 4b was found to be most potent elastase inhibitor (IC50 = 0.41 ± 0.01 µM) amongst the synthesized series against standard Oleanolic Acid (IC50 value = 13.45 ± 0.0 µM). The Kinetics mechanism for compound 4b was analyzed by Lineweaver-Burk plots which revealed that compound inhibited elastase competitively by forming an enzyme-inhibitor complex. Along with this, all the synthesized compounds (4a - 4j) exhibits excellent DPPH free radical scavenging ability. The inhibition constant Ki for compound 4b was found to be 0.6 µM. The computational study was comprehensible with the experimental results with good docking energy values (Kcal/mol). Therefore, these molecules can be considered as promising medicinal scaffolds for the treatment of skin-related maladies.