In this paper, conformal minimal 2-sphere immersed in a complex projective space are studied by applying Lie theory, moving frame and harmonic sequence. First, we use a different way from Bolton to prove that a holomorphic curve from S² into CPⁿ is uniquely determined by its induced metric, up to a rigid motion. Secondly, via conformal minimal immersions of constant curvature from S² into CPⁿ, we can construct new minimal immersions of S² in G_2,n+1 with constant curvature. Finally, if φ is a totally real conformal minimal 2-sphere of constant curvature immersed in a complex projective space, then we can find the explicit isometry transform ｇ such that ｇφ lies in RPⁿ CP^n.