Boiling Liquid Expanding Vapour Explosions (BLEVEs) are driven by complex fluid dynamics with expanded vapour and flashed liquid. They may generate strong shock waves that lead to catastrophic consequences to personnel and structures in the vicinity. Despite the great interest in safety management and intensive research efforts, reliable and efficient prediction of BLEVE loads on structures is still challenging in practice. Computational Fluid Dynamics (CFD), based on complex physics formulas, can provide more accurate predictions of BLEVE loads than the traditional empirical and TNT-equivalency approaches, but suffers from high computational costs. Data-driven machine learning models offer efficient surrogates but conventional models, including commonly used multi-layer perceptron (MLP), are suboptimal especially for explosions of complex geometry and in complex environment. In this study, a novel machine learning approach, based on the state-of-the-art Transformer neural networks, is developed for BLEVE loads prediction on an idealised structure in the vicinity of BLEVE. Through extensive experiments and rigorous evaluation, it is shown that Transformer can effectively model the structure-wave interaction, yielding accurate pressure and impulse predictions with less than 14% relative errors, which outperforms widely used MLP (20% error) significantly. The developed Transformer model is applied to predict critical parameters of BLEVE loads, including arrive time, rise time and duration. The results demonstrate that Transformer can produce an accurate pressure-time history, yielding a comprehensive characterisation of BLEVE loads on structures.