The spiral fin-and-tube heat exchanger is a widely used heat transfer device in heating and cooling applications, and its performance is influenced by multiple structural parameters, including the pitch, thickness, and height of the fins, the diameter and thickness of the base tube, and the transverse and longitudinal tube spacings. This study comprehensively explores how these factors affect the heat transfer performance of the spiral fin-and-tube heat exchanger and aims to determine its optimal configuration of structural parameters. First, orthogonal experiments are arranged based on these factors to conduct the corresponding finite element numerical simulations and to determine the effects of these factors on the heat transfer and resistance performance of the spiral fin-and-tube heat exchanger. Subsequently, support vector regression (SVR) is introduced to predict the heat transfer factor and the resistance factor, with the aim of benefiting the construction of a multi-objective optimization model for optimizing the two factors simultaneously. Then, a comprehensive performance indicator is used to transform the multi-optimization problem to a single optimization problem, and the genetic algorithm is adopted to solve an optimal configuration of the heat exchanger structural parameters. Ultimately, the finite element numerical simulation is utilized to validate the accuracy of the optimization. Case studies are conducted on a specific spiral fin-and-tube heat exchanger. After the optimization, the heat transfer factor is improved by 44.44%, and the resistance factor is increased by 14.19%. However, the comprehensive performance indicator is increased by 38.79%.