The importance of examining the wake effect of wind farms for optimizing their layout and augmenting their power generation efficiency is immense. Considering that the establishment of extensive wind farms often leads to a significant number of turbines being positioned downstream of preceding ones, it significantly diminishes their power generation efficiency. In our study, we propose a graph representation learning model with improved Transformer (GRL-ITransformer) to better integrate feature information, so that the model can capture the dynamic time relationship of different variables and establish its spatial relationship, striving to enhance the precision in predicting wind turbine wake field. Different from the previous way involving handling reduced-order and separating prediction process, we combine the reduced-order technique with the proposed model to make the model more efficiently and intelligently determine the number of modes required for model prediction. After that, the data driven method is employed to update the parameters, and the superiority of GRL-ITransformer is highlighted by analyzing and comparing with the existing five classical intelligent algorithms (belongs to four categories). The comprehensive results show that GRL-ITransformer has excellent performance in wind turbine wake field prediction and reconstruction, and always possesses the lowest error for a series of error evaluation indexes among all models.