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This study presents the development of a finite element method (FEM) surrogate model based on a convolutional neural network (CNN) for iterative prediction of deformation behavior in the H-beam rolling process. The H-beam rolling process involves complex, multi-pass deformation that requires precise geometric control, making traditional FEM simulations computationally expensive and time-consuming. To address these challenges, we generated training data using a fractional factorial design and three-dimensional FEM simulations. The data, initially at the node level, was transformed into images through Delaunay triangulation, allowing the CNN to predict material shape, temperature, and equivalent strain (EQ-strain) after each roll pass. Process conditions were incorporated as a mask layer, reducing error accumulation during iterative predictions and improving overall prediction accuracy. The surrogate model demonstrated high performance, achieving a shape F1-score of 0.9801 in continuous prediction sequences and reducing prediction time from 32 hours to 0.85 seconds compared to traditional FEM. The model achieved a MAPE of 3.6570% for temperature and 34.1324% for EQ-strain in iterative predictions, with error levels that were lower than expected. This research represents the first successful application of a CNN-based FEM surrogate model for multi-step continuous processes like H-beam rolling, offering significant potential for real-time process optimization in industrial settings.