Novel peptides useful as a therapeutic and/or prophylactic agent of cancers, as well as medical uses thereof, are described. Each of these peptides have a consecutive amino acid sequence within a specific region of YKL-40 antigen expressing on the cell surface of brain tumor cells, that is, within the region aa10-19, aa49-61, aa74-83, aa96-117, aa152-161, aa177-185, aa202-211, aa246-261 or aa326-354, which peptide has an immunity-inducing activity. These peptides are useful for therapy and/or prevention of cancers when administered to a living body, and are useful for inducing T cells which exert cytotoxic activity against cancer cells when used to stimulate the T cells in vitro.