The method of treating delayed healing of a wound associated with diabetes includes administering to the wound a composition comprising an anti-senescence compound and a pharmaceutically acceptable carrier. The anti-senescence compound may be 18α-Glycyrrhetinic acid, a Caveolin-1 (Cav-1) inhibitory compound, or a Polymerase I Transcript Release Factor (PTRF-1) inhibitory compound. The anti-senescence compound may be effective in preventing and/or reversing premature cellular senescence. The anti-senescence compound may be effective in promoting healing of a wound, e.g., delayed or incompletely healed wound. The anti-senescence compound may be effective in promoting healing of a delayed healing wound or chronic wound of a diabetic patient, such as a diabetic ulcer or venous ulcer.