Electrospun membranes are widely used in bone tissue engineering because of their similar bone extracellular matrix. The morphological characteristics of electrospun membranes, which include fibre diameter and alignment, play crucial roles in determining cellular behaviour and osteogenesis. Therefore, to investigate the effects of these two parameters on bone marrow mesenchymal stem cells (BMSCs), we prepared electrospun poly-L-lactic acid membranes using different diameters (nanoscale and microscale) and alignments (aligned and random) to investigate the effects of different surface morphologies on the proliferation, adhesion, migration, cell morphology, and osteogenesis of BMSCs. Our results showed that electrospun membranes with different surface morphologies have good biocompatibility and can regulate cell morphology, and the parallel aligned fibre orientation can promote cell migration. More importantly, BMSCs cultured on aligned nanofibres have a higher osteogenic potential than aligned microfibres and random fibres. Furthermore, our study shows that the surface morphology of electrospun membranes, which is one of the characteristics of biomaterials, can regulate the cellular behaviour of BMSCs, and that aligned nanofibre electrospun membranes can contribute to promoting osteogenesis, which can be used as the surface morphology of bone repair materials.