Disclosed are: a process for producing a fermented milk which can produce a specific peptide having useful functions (e.g., anti-hypertensive effect) in a fermented milk with good efficiency and can impart excellent flavor and functional activities (e.g., anti-hypertensive activity) to a fermented milk beverage/food in a simple manner； and a fermented milk beverage/food having excellent flavor and functional activities which is produced by using the fermented milk. The process comprises the combination of step (A) with step (B): step (A) in which an animal milk casein is enzymatically digeste with a protease (1) including a specific protease (e.g., papain)； and step (B) in which an animal milk casein or the like is fermented with lactic acid bacterium to thereby produce VPP, IPP and YP. The fermented milk beverage/food comprises the fermented milk produced by the process or a condensation product thereof and contains VPP, IPP and YP in given amounts or more in terms of the amounts determined upon drinking.
