Bioresorbable electrospun fibres have highly functional features that can preserve drug efficacy, avoiding premature degradation, and control drug release rates over long periods. In parallel, it is known that Alzheimer’s disease (AD) has been linked to impaired insulin signalling in the brain. Glucagon-like peptide 1 (GLP-1) analogues have beneficial effects on insulin release and possess exceptional neuroprotective properties. Herein, we describe for the first time the incorporation of a GLP-1 analogue, liraglutide, into electrospun poly (lactic acid) (PLA) fibres with in situ gelatin capsules, in order to provide the controlled release of liraglutide, improving neuroprotective properties. In this study, PLA, a bioresorbable polymer in which degradation products have neurogenesis characteristics, was electrospun and loaded with liraglutide. Moreover, PLA/liraglutide fibres were encapsulated with gelatin and were shown to have better properties than the non-encapsulated fibres in terms of the controlled release of liraglutide, which was accomplished in the present study for up to 60 days. We observed that this biodevice was completely encapsulated with gelatin, which made the material more hydrophilic than PLA fibres alone and the biodevice was able to enhance fibroblast interaction and reduce mitochondrial stress in a neuroblastoma cell line. In this manner, this study introduces a new material which can improve neuroprotective properties from AD oxidative stress via the sustained long-lasting release of liraglutide.