Magnetic field prediction is a core aspect of magnet design, yet traditional finite element methods (FEM) face computational bottlenecks when handling complex structures. This paper proposes a DeepONet-based surrogate modeling approach for magnetic field prediction, designed to efficiently map coil structural parameters to spatial magnetic field distributions. The model employs a dual-branch input network that separately encodes coil geometric features and spatial coordinate information, subsequently outputting each magnetic field component. Through validation on representative coil cases featuring symmetric and asymmetric cross-sections, the model demonstrates prediction accuracy comparable to FEM while achieving significantly accelerated computational efficiency. Results indicate that the proposed method exhibits strong structural adaptability and generalization capabilities, providing an efficient solution for optimized magnet design.