In construction engineering, transportation is a key factor affecting the construction schedule, and Transportation Speed Prediction (TSP) provides essential information for the precise scheduling of construction transportation. TSP is a challenging task due to the complex spatial-temporal traffic correlations and the dynamic variation of transportation routes. Given the superiority in topology representation of traffic networks, graphbased networks are becoming the prevalent traffic prediction solutions. However, existing methods have difficulty in dealing with dynamic transportation network structures and insufficiency in extracting representative spatial-temporal features. To address such issues, in this article, an Adaboosting Graph Attention Recurrent Network (Ada-GARN) is proposed. In the network, a graph attention recurrent unit is developed that integrates graph attention convolution with gated recurrent structures to extract spatial-temporal features of the transportation network with changing structures. On this basis, considering the effect of the time lag in traffic propagation, the attention space of graph convolution is extended to the past state of neighboring nodes based on traffic feature graphs, which enhances the representation of spatial evolution characteristics. Furthermore, to effectively integrate the multi-scale spatial-temporal information, the model uses an Adaboost framework to ensemble graph attention recurrent units instead of directly stacking spatial-temporal layers, which measures the feature differences among layer-wise neighbors and adaptively adjusts node weights in training. Experiments conducted on a large infrastructure project transportation dataset and a highway dataset show the model's adaptability to different scenarios. The proposed model outperforms state-of-the-art methods and reduces 11.2%-28% and 23%-23.1% in terms of RMSE and MAE metrics, respectively.