The present invention provides methods for inducing, maintaining and expanding CTL (cytotoxic T cell) having an antigen-specific cytotoxic activity at a high level, which is useful in the adoptive immunotherapy, by using as an effective ingredient at least one compound selected from the group consisting of acidic polysaccharides, acidic oligosaccharides, acidic monosaccharides, and salts thereof. The above-mentioned compounds include fucoidans, heparins, alginic acid, chondroitin sulfate A, chondroitin sulfate B, pectic acid, hyaluronic acid, degradation products of fucoidans, sulfated glucose, sulfated fucose and salts thereof.