Using optimal assembly relationships, companies can enhance product quality without significantly increasing production costs. However, predicting Assembly Geometric Errors presents a challenging real-world problem in the manufacturing domain. To address this challenge, this paper introduces a highly efficient Transformer-based neural network model known as Predicting Assembly Geometric Errors based on Transformer (PAGEformer). This model accurately captures long-range assembly relationships and predicts final assembly errors. The proposed model incorporates two unique features: firstly, an enhanced self-attention mechanism to more effectively handle long-range dependencies, and secondly, the generation of positional information regarding gaps and fillings to better capture assembly relationships. This paper collected actual assembly data for folding rudder blades for unmanned aerial vehicles and established a Mechanical Assembly Relationship Dataset (MARD) for a comparative study. To further illustrate PAGEformer performance, we conducted extensive testing on a large-scale dataset and performed ablation experiments. The experimental results demonstrated a 15.3% improvement in PAGEformer accuracy compared to ARIMA on the MARD. On the ETH, Weather, and ECL open datasets, PAGEformer accuracy increased by 15.17%, 17.17%, and 9.5%, respectively, compared to the mainstream neural network models.