An advanced superconducting ECR ion source named SECRAL has been constructed at Institute of Modern Physics of Chinese Academy of Sciences,whose superconducting magnet assembly consists of three axial solenoid coils and six sextupole coils with a cold iron structure as field booster and clamp.In order to investigate the structure of sextupole coils and to increase the structural reliabilities of the magnet system, global and local structural analysis have been performed in various operation scenarios.Winding pack and support structure design of magnet system,mechanical calculation and stress analysis are given in this paper. From the analysis results,it has been found that the magnet system is safe in the referential operation scenarios and the configuration of the magnet complies with design requirements of the SECRAL.