We report the late-time evolution of Type IIb supernova (SN IIb) 2013df. SN 2013df showed a dramatic change in its spectral features at similar to 1 yr after the explosion. Early on it showed typical characteristics shared by SNe IIb/Ib/Ic dominated by metal emission lines, while later on it was dominated by broad and flat-topped Ha and He I emissions. The late-time spectra are strikingly similar to SN IIb 1993J, which is the only previous example clearly showing the same transition. This late-time evolution is fully explained by a change in the energy input from the Co-56 decay to the interaction between the SN ejecta and dense circumstellar matter (CSM). The mass-loss rate is derived to be similar to(5.4 +/- 3.2) x 10(-5) M(circle dot)yr(-1) (for the wind velocity of similar to 20 km s(-1)), similar to SN 1993J but larger than SN IIb 2011dh by an order of magnitude. The striking similarity between SNe IIb 2013df and 1993J in the (candidate) progenitors and the CSM environments. and the contrast in these natures to SN 2011dh. infer that there is a link between the natures of the progenitor and the mass loss: SNe IIb with a more extended progenitor have experienced a much stronger mass loss in the final centuries toward the explosion. It might indicate that SNe IIb from a more extended progenitor are the explosions during a strong binary interaction phase, while those from a less extended progenitor have a delay between the strong binary interaction and the explosion.