This paper and its sequel present a denotational semantic descriptive method based on trace. The method combines characteristics of operational semantics and algebraic semantics, avoids domain theory as the theoretical basis, and unites static semantic and dynamic semantic description. It is contended that the new method is more suitable to be used to deal with real programming language by using it to define semantics of a middle-scale Algol-like model language. In this paper, the concept of trace is introduced first, then a model language is given and the corresponding semantic domains are defined without using recursive domain equations.