Have you compared your coin here? http://www.varietyvista.com/01b LC Doubled Dies Vol 2/DDO 1988-D.htm
If you notice the ridge inside the rim on the left side of the cent, that's an indication that the die is very worn which results (in most cases) in the doubling you are seeing. In the link provided by @alurid, you can see the split serifs on the 9 and the mint mark which I don't see on your coin.