The equivariant CR minimal immersions from the round 3-sphere $$S^3$$ S3 into the complex projective space $$\mathbb CP^n$$ 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 $$S^3=\mathrm{SU}(2)$$ S3=SU(2) endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra $$\mathfrak {su}(2)$$ su(2) , we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere $$S^3$$ S3 into $$\mathbb CP^n$$ CPn without the assumption of constant sectional curvatures.