An approach of generalized optimum ordering is proposed considering the problem of dynamic multi-attribute decision making with incomplete decision information in practice. The decision problem is transformed into the matrix problem of generalized optimum ordering number. Meanwhile, a new method of determining the dynamic weight including both attribute-weight and time-weight is given based on the idea of TOPSIS, which reflects the subjective preference of the decision maker and the importance of the attributes and time-samples, making the decision results coincident with the desire of decision makers. Finally, an example is given to show the feasibility and effectiveness of the proposed theory.