The present invention relates to a method for cultivation and manufacturing efficiently algae containing useful substances in cells thereof in a high concentration. According to conventional cultivation apparatus, shear stress applied to algae causes difficulty of high density cultivation; however, by cultivation of algae by using a convenient cultivation apparatus having a dome shape, conical shape, or cylindrical shape and made by a clear material, high density cultivation has been realized without shear stress. The present cultivation apparatus realizes more efficient cultivation in combined use with a separate gas discharging apparatus. In addition, the present invention can be applied to a wide variety of algal species having ability to produce highly unsaturated fatty acid, a photosynthetic pigment, or a polysaccharide.