The additive manufacturing of natural fibre-reinforced polymers is a pivotal method in developing sustainable engineering solutions. Using the fused filament fabrication method, the current study investigates the additive manufacturing of hemp-reinforced polybutylene succinate (PBS) alongside its mechanical characterization. Two types of hemp reinforcement are considered: short fibres (max. length smaller than 2 mm) and long fibres (max. length smaller than 10 mm), which are compared against non-reinforced (pure) PBS. A detailed analysis is performed regarding the determination of suitable 3D printing parameters (overlap, temperature, nozzle diameter). In a comprehensive experimental study, additionally to general analyses regarding the influence of hemp reinforcement on the mechanical behaviour, the effect of printing parameters is determined and discussed. Introducing an overlap in the additive manufacturing of the specimens results in improved mechanical performance. The study highlights that the Young’s modulus of PBS can be improved by 63% by introducing hemp fibres in conjunction with overlap. In contrast, hemp fibre reinforcement reduces the tensile strength of PBS, while this effect is less pronounced considering overlap in the additive manufacturing process.