Looks like it contains mineral oil:
Water, Tocopheryl Acetate, Mineral Oil, Stearic Acid, Glyceryl Stearate, Cetyl Alcohol, Propylene Glycol, Isopropyl Palmitate, Triethanolamine, Disodium EDTA, Dimethicone, Diazolidinyl Urea, Methylparaben, Propylparaben.
That being said, not all acne is caused by oil - for a while I was washing with Castor & Jojoba twice a week and it really did nice things for unclogging pores. You can google the oil cleaning method (OCM) for more info. I think I'll actually start that up again soon.