The discovery of three-dimensional (3D) topological insulators opens a gateway to generate unusual phases and particles made of the helical surface electrons, proposing new applications using unusual spin nature. Demonstration of the helical electron transport is a crucial step to both physics and device applications of topological insulators. Topological insulator nanowires, of which spin-textured surface electrons form 1D band manipulated by enclosed magnetic flux, offer a unique nanoscale platform to realize quantum transport of spin-momentum locking nature. Here, we report an observation of a topologically protected 1D mode of surface electrons in topological insulator nanowires existing at only two values of half magnetic quantum flux (±h/2e) due to a spin Berry's phase (π). The helical 1D mode is robust against disorder but fragile against a perpendicular magnetic field breaking-time-reversal symmetry. This result demonstrates a device with robust and easily accessible 1D helical electronic states from 3D topological insulators, a unique nanoscale electronic system to study topological phenomena.