As traditional description logic systems are not good at representing uncertain (or vague) knowledge, this paper introduces lower approximation and upper approximation which are based on the rough set semantics to description logic systems, and extends the traditional description logic in a simple way. It introduces the concept of rough description logic, in the systems of which we can use appropriate subconcept and superconcept to express some vague knowledge. This paper focuses on the rough extension of the description logic ALC and introduces the syntax, semantics and related reasoning problems of the rough description logic RALC obtained after extension, and then discusses the basic idea of modeling imprecise concepts using the rough description logic. Finally, the paper presents a reasoning algorithm of the satisfiability problem of RALC. This task can make formal descriptions and reasoning of uncertain knowledge in the description logic more convenient.