A graph G is fractional [a, b]-covered if for any e ∈ E(G), G possesses a fractional [a, b]-factor including e. A graph G is fractional (a, b, k)-critical covered if G − Q is fractional [a, b]-covered for any Q ⊆ V(G) with |Q| = k. In this paper, we verify that a graph G of order n is fractional (a, b, k)-critical covered if n ≥ (a+b)((2r−3)a+b+r−2)+bk+2 b , δ(G) ≥ (r − 1)(a + 1) + k and max{d G (w 1), d G (w 2), · · · , d G (w r)} ≥ an + bk + 2 a + b for every independent vertex subset {w 1 , w 2 , · · · , w r } of G. Our main result is an improvement of the previous result [S. Zhou, Y. Xu, Z. Sun, Degree conditions for fractional (a, b, k)-critical covered graphs, Information Processing Letters 152(2019)105838].