Severe liver disease is one of the most common causes of death globally. Currently, whole organ transplantation is the only therapeutic method for end-stage liver disease treatment, however, the need for donor organs far outweighs demand. Recently liver tissue engineering is starting to show promise for alleviating part of this problem. Electrospinning is a well-known method to fabricate a nanofibre scaffold which mimics the natural extracellular matrix that can support cell growth. This study aims to investigate liver cell responses to topographical features on electrospun fibres. Scaffolds with large surface depression (2 μm) (LSD), small surface depression (0.37 μm) (SSD), and no surface depression (NSD) were fabricated by using a solvent–nonsolvent system. A liver cell line (HepG2) was seeded onto the scaffolds for up to 14 days. The SSD group exhibited higher levels of cell viability and DNA content compared to the other groups. Additionally, the scaffolds promoted gene expression of albumin, with all cases having similar levels, while the cell growth rate was altered. Furthermore, the scaffold with depressions showed 0.8 MPa higher ultimate tensile strength compared to the other groups. These results suggest that small depressions might be preferred by HepG2 cells over smooth and large depression fibres and highlight the potential for tailoring liver cell responses.