In this study, the efficient ZSM-5 zeolite/polycaprolactone-polyethylene glycol nanofibers (PCL-PEG NFs) were developed for the combined sustained release of dexamethasone (DEX), and ascorbic acid (ASC) to enhance the osteoblastic differentiation of human adipose-derived stem cells (hADSCs). The fabricated NFs were evaluated by BET/BJH, FTIR, and FE-SEM analyses. This composite DEX/ASC@ZSM-5/PCL-PEG electrospun NFs revealed that the initial burst drug release was rather reduced by loading the drug into the ZSM-5 zeolites, resulting in a sustained and prolonged drug release from NFs. The results of FE-SEM, MTT and PicoGreen assays, qPCR, and alkaline phosphatase (ALP) assays confirmed hADSCs cultured on the DEX/ASC@ZSM-5/PCL-PEG NFs had superior cell adhesion, metabolic activity, and proliferation percentage compared to other forms of NFs after 14 and 28 days of incubation. In the meantime, DEX and ASC displayed high osteogenic differentiation capability when they impacted on hADSCs. These results indicated that ZSM-5/NFs could be used to develop a novel platform for bone tissue regeneration and engineering by facilitating of the sustained/controlled release of therapeutic compounds.