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The MJ-class superconducting magnetic energy storage system (SMES) is most likely put into commercial utility applications. In China, several 1–100-MJ-class high-temperature superconducting (HTS) SMES projects are undergoing preresearch and conceptual design stage by the government and the power grid corporations, and these SMESs will be developed later. The configurations of commonly used SMES magnets are single-solenoid, multiple-solenoid, and toroidal magnets. Each configuration has its own electromagnetic and mechanical characteristics. In this paper, an optimal design and comparison were carried out to explore the suitable configuration for the MJ-class SMES magnet. As the critical current of the conductor is strongly influenced by the magnetic field and its applied direction, optimization of the HTS coil's configuration is required to minimize the length of the HTS wire. The optimization was conducted with the genetic algorithm and the finite-element method. In order to find the dependence of energy storage capacity on the wire cost, the magnet schemes of seven energy requirements were investigated. An optimal design is performed for the seven stored energies with the three types of magnet configurations. The comparisons between single-solenoid, four-solenoid, and toroidal coils are presented. The magnetic field and stress distribution of the SMES magnet are also depicted. [ABSTRACT FROM PUBLISHER]