The logarithm function, with a slight modification, is proposed to be a general utility function for decision making under risk or uncertainty with known probability distribution. This utility function, as based on this author's concept of relative value, is mathematically and philosophically justified. It is shown that one normalized utility function or curve can be used for different problems, and also for the same problem with different degrees of personal preference of risk-aversion. It is also shown that the linear case with a straight-line utility function, in which the expected reward (ER) criterion and the expected loss (EL) criterion can be applied, is a special case of this proposed general utility function. A simple example is worked out for illustration.