Excessive load sway is a critical safety concern during crane operations, exposing cranes to risks of instability and collision with surrounding objects. Existing methods for predicting load sway struggle with inefficiency and inaccuracy. Advances in robotics and automation have led to the robotisation of cranes, enhancing both safety and efficiency. This paper proposed a physics-informed neural network (PINN) for predicting the load sway of autonomous mobile cranes (AMCs) in base-moving conditions, and introduced a transfer learning (TL) framework to address complexities in AMC dynamics while reducing the need for extensive training data. Initially trained on numerically simulated data with simplified dynamics, the PINN was subsequently fine-tuned using real-world data, which included realistic dynamic uncertainties and complexities. Numerical simulations and laboratory experiments were conducted to validate the PINN’s performance. The proposed PINN accurately predicted payload motion and maintained robust performance in both numerical simulations and laboratory experiments while exhibiting superior computational efficiency, requiring only 12.5% of the time needed by traditional dynamic models for 1 s prediction windows. Furthermore, it was compared and outperformed other machine learning models, including recurrent neural networks (RNN), long short-term memory (LSTM) networks and multilayer perception (MLP). These findings indicate that the proposed PINN provides a robust and efficient solution for sensorless load sway prediction in crane operations. • Developed a PINN for autonomous mobile cranes (AMCs) load sway prediction. • Introduced a TL framework to address complexities in AMCs dynamics. • Validated through numerical simulation and laboratory experiments. • Cross-compared three normalisation methods and ten activation functions. • Benchmarked against ML methods, such as RNN, LSTM and MLP.