In this paper, the Schur convexity is generalized to Schur $f$-convexity, which contains the Schur geometrical convexity, harmonic convexity and so on. When $f$ : ${mathbb{R}}_+{ ightarrow}{mathbb{R}}$ is defined as $f(x)=(x^m-1)/m$ if $m{ eq}0$ and $f(x)$ = ln $x$ if $m=0$, the necessary and sufficient conditions for $f$-convexity (is called Schur $m$-power convexity) of Gini means are given, which generalize and unify certain known results.