Hofmeister anion effects on adsorption kinetics of the positively charged lysozyme (pH < pI) at an air-water interface were studied by surface tension measurements and time-resolved X-ray reflectometry. In the salt-free solution, the protein adsorption rate increases with decreasing the net positive charge of lysozyme. When salt ions are dissolved in water, the protein adsorption rate drastically increases, and the rate is following an inverse Hoffmeister series (Br(-) > Cl(-) > F(-)). This is the result of the strongly polarized halide anion Br(-) being attracted to the adsorbed protein layer due to strong interaction with local electric field, while weakly polarized anion F(-) having no ability to penetrate the protein layer. In X-ray reflection studies, we observed that the lysozyme molecules initially adsorbed on the air-water interface have a flat unfolded structure as previously reported in the salt-free solution. In contrast, in the concentrated salt solutions, the lysozyme molecules begin to refold during adsorption. This protein refolding as a result of protein-protein rearrangements may be a precursor phenomenon of crystallization. The refolding is most significant for Cl(-), which is a good crystallization agent, whereas it is less observed for the strongly hydrated F(-). It is widely known in the bulk state that kosmotropic anions tend to precipitate proteins but at the same time stabilize proteins against denaturing. On the other hand, at the air-water interface where adsorbed proteins usually unfold, we observed chaotropic anions strongly bound to proteins that reduce electrostatic repulsion between protein molecules, and subsequently they induce protein refolding whereas the kosmotropic anions do not.