Provided are acidic hair dye compositions in which the dye has a high permeability into hair, the dye can be applied uniformly, and the composition has excellent staining property, safety and sense of use at the time of hair dyeing. The acidic hair dye compositions of the present invention comprise at least one dibasic acid ester compound represented by general formula I below: wherein, in general formula I, R1 is an alkylene group which may have a substituent with 2 to 4 carbon atoms, R2 and R3 are, independently from each other, an alkyl group which may have a substituent with 1 to 4 carbon atoms, R4 and R5 are, independently from each other, hydrogen, methyl group or ethyl group, m and n is, independently from each other, an integer of 0 to 4, wherein m+n≧1 (with the proviso that the case is excluded in which R2 and R3 are both ethyl group, and m and n are both 1).