Band convergence is considered to be a strategy with clear benefits for thermoelectric performance, generally favoring the co-optimization of conductivity and Seebeck coefficients, and the conventional means include elemental filling to regulate the band. However, the influence of the most electronegative fluorine on the CoSb3 band remains unclear. We carry out density-functional-theory calculations and show that the valence band maximum gradually shifts downward with the increase of fluorine filling, lastly the valence band maximum converges to the highly degenerated secondary valence bands i...