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Bi-6p electrons are well known to possess a strong spin–orbit interaction, but a mass correction based on the relativistic effect is scarcely discussed in the electronic state. To clarify the relativistic properties of Bi-6p electrons, we grew single crystals of SrBi₃ with the AuCu₃-type cubic structure by the Bi self-flux method and carried out electrical resistivity, specific heat, and de Haas–van Alphen (dHvA) experiments. Several kinds of closed Fermi surfaces are observed from the dHvA effect. Among them, three kinds of main Fermi surfaces are compared with the results of full-potential linearized augmented plane wave (FLAPW) energy band calculations under two considerations. One corresponds to the mass correction in the spin–orbit interaction for Bi-6p electrons. The other is without the mass correction. Detected two kinds of the main Fermi surfaces are well explained with and without the mass correction, but a remaining Fermi surface is explained only with the mass correction. The relativistic effects of the spin–orbit interaction and mass correction are essentially important for Bi-6p electrons in SrBi₃.