On the new findings that cyclodextrin shows no cytotoxicity or only slight cytotoxicity on cell growth and that lipophilic substances such as unsaturated fatty acids and lipophilic vitamins when present together with, or included in, cyclodextrin show such effects as cell growth promoting effect and accelerating effect of the productivity of valuable products, a serum-free or serum-reduced culture medium or a substitute composition for serum for a culture medium comprising a cyclodextrin and at least one lipophilic nutrient substance, said cyclodextrin and said lipophilic nutrient substance being preferably in the form of inclusion complex between them, is provided.