In addition to various functions, hydrogels used to promote wound healing should also have good biocompatibility, stability and mild degradability. Therefore, we designed and synthesized aldehyde modified aliphatic cyclic carbonate monomer (MTC-Ba). Then the hydrogel matrix (MTC-Ban-b-PEG6k-b-MTC-Ban, MBP) was prepared by ring opening polymerization using polyethylene glycol (PEG) as the initiator and hydrophilicity enhancer. The matrix was covalently linked with the crosslinker adipic acid dihydrazide (ADH) through dynamic hydrazide bond to form a self-healing hydrogel (SH-Gel). At the same time, curcumin was loaded into the hydrogel as a functional model drug. The resulting hydrogel has porosity, injectability, appropriate swelling rate, friendly cell compatibility and safe degradability. In addition, in vivo wound healing evaluation, histological evaluation and immunofluorescence staining showed that this gel could the wound closure, re-epithelium and collagen regeneration. In conclusion, this study provides a new choice for the application of synthetic biodegradable polymer materials in promoting skin wound healing.