The equivariant CR minimal immersions from the round 3-sphere S3 into the complex projective space CPn have been classified by the third author explicitly (Li in J Lond Math Soc 68:223–240, 2003). In this paper, by employing the equivariant condition which implies that the induced metric is left-invariant and that all geometric properties of S3 = SU(2) endowed with a left-invariant metric can be expressed in terms of the structure
constants of the Lie algebra su(2), we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere S3 into CPn without the assumption of constant sectional curvatures.

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