The fast assessment of the global minimum adsorption energy (GMAE) between catalyst surfaces and adsorbates is crucial for large-scale catalyst screening. However, multiple adsorption sites and numerous possible adsorption configurations for each surface/adsorbate combination make it prohibitively expensive to calculate the GMAE through density functional theory (DFT). Thus, we designed a multi-modal transformer called AdsMT to rapidly predict the GMAE based on surface graphs and adsorbate feature vectors without site-binding information. The AdsMT model effectively captures the intricate relationships between adsorbates and surface atoms through the cross-attention mechanism, hence avoiding the enumeration of adsorption configurations. Three diverse benchmark datasets were introduced, providing a foundation for further research on the challenging GMAE prediction task. Our AdsMT framework demonstrates excellent performance by adopting the tailored graph encoder and transfer learning, achieving mean absolute errors of 0.09, 0.14, and 0.39 eV, respectively. Beyond GMAE prediction, AdsMT's cross-attention scores showcase the interpretable potential to identify the most energetically favorable adsorption sites. Additionally, uncertainty quantification was integrated into our models to enhance the trustworthiness of the predictions.