We have performed molecular dynamics (MD) simulations of the protein alpha-lactalbumin in aqueous solution containing the ionic liquid (IL) 1-butyl-3-methyl imidazolium tetrafluoroborate ([BMIM][BF4]) as the cosolvent at different concentrations. Attempts have been made to obtain quantitative understanding of the effects of the IL on the conformational features of the protein as well as the distributions of the IL and water around it. The calculations revealed enhanced rigidity of the protein with reduced conformational fluctuations and increasingly correlated local motions in the presence of the IL. Nonuniform relative population of the BMIM+ and BF4(-) ions at the protein surface with respect to that in the bulk solution has been observed. It is demonstrated that exchange of water by the IL around the protein results in rearrangement of the hydrogen bond network at the interface with breaking of protein-water hydrogen bonds and formation of protein-IL hydrogen bonds. Importantly, it is found that the protein forms increased number of stronger salt bridges in the presence of IL. This shows that the formation of a greater number of such stronger salt bridges is the origin behind the enhanced rigidity of the protein in the presence of the IL.