In this study, we demonstrate the possibility to tune Dirac surface states of a three-dimensional topological insulator (TI) by applying external strain to single-crystalline Bi2Se3 nanowires (NWs). The NWs were placed over 200 nm deep trenches, which leads to a significant bending, resulting in tensile strain at the bottom surface of the wire and compressive strain at its top surface. By performing low-temperature magnetotransport measurements, we were able to show that TI surfaces under compressive or tensile strain (ϵ=±0.1%) experience a significant Dirac shift of ΔE=∓30 meV as compared to relaxed surfaces. For surface states under tensile strain, an increased carrier mobility is indicated. The opportunity to externally tune the Dirac states therefore could lead to further improvement in future TI devices.