We present a dynamic description logic for representation and reasoning about actions, with an approach that embrace actions into the description logic . With this logic, description logic concepts can be used for describing the state of the world, and the preconditions and effects of atomic actions; Complex actions can be modeled with the help of standard action operators, such as the test, sequence, choice, and iteration operators; And both atomic actions and complex actions can be used as modal operators to construct formulas. We develop a terminable and correct algorithm for checking the satisfiability of formulas. Based on the algorithm, many reasoning tasks on actions are effectively carried out, including the realizability, executability, projection and planning problems.