  A graph $G$ is a fractional $(a,b,k)$-critical covered graph if $G-U$ is a
fractional $[a,b]$-covered graph for every $U\subseteq V(G)$ with $|U|=k$,
which is first defined by Zhou, Xu and Sun (S. Zhou, Y. Xu, Z. Sun, Degree
conditions for fractional $(a,b,k)$-critical covered graphs, Information
Processing Letters, DOI: 10.1016/j.ipl.2019.105838). Furthermore, they derived
a degree condition for a graph to be a fractional $(a,b,k)$-critical covered
graph. In this paper, we gain an independence number and connectivity condition
for a graph to be a fractional $(a,b,k)$-critical covered graph and verify that
$G$ is a fractional $(a,b,k)$-critical covered graph if $$
\kappa(G)\geq\max\Big\{\frac{2b(a+1)(b+1)+4bk+5}{4b},\frac{(a+1)^{2}\alpha(G)+4bk+5}{4b}\Big\}.
$$
