Future trajectory prediction of a tracked pedestrian from an egocentric perspective is a key task in areas such as autonomous driving and robot navigation. The challenge of this task lies in the complex dynamic relative motion between the ego-camera and the tracked pedestrian. To address this challenge, we propose an ego-motion-guided trajectory prediction network based on the Mamba model. Firstly, two Mamba models are used as encoders to extract pedestrian motion and ego-motion features from pedestrian movement and ego-vehicle movement, respectively. Then, an ego-motion guided Mamba decoder that explicitly models the relative motion between the pedestrian and the vehicle by integrating pedestrian motion features as historical context with ego-motion features as guiding cues to capture decoded features. Finally, the future trajectory is generated from the decoded features corresponding to the future timestamps. Extensive experiments demonstrate the effectiveness of the proposed model, which achieves state-of-the-art performance on the PIE and JAAD datasets.