The invention relates to a process for producing cream from milk, which includes carrying out a membrane concentration of the milk, then carrying out a separation of the cream from the milk, and then carrying out a pasteurization of the cream, in which the process further includes decreasing a dissolved oxygen concentration in the milk before the pasteurization using a deoxygenation membrane and further relates to a process for producing fatty food or fat-containing food by using the cream as a raw material, and the cream having an excellent flavor and physical properties, the fatty food having a good flavor, and the fat-containing food having a good flavor, which can be obtained by the processes.