In this paper, we develop a method for multiperiod multiattribute decision-making (MP-MADM) problems, in which the decision information, including attribute weights and attribute values, is given at different periods. First, using the variation in attribute values of the various alternatives for unit time, we can obtain the trend incentive coefficient of variation that represents reward or punishment for the development tendency of alternatives. This paper proposes a method based on maximum entropy ordered weighted averaging (MEOWA) to determine the trend incentive coefficient. Second, considering the differences development tendency of the alternatives, we propose an approach that integrates the trend incentive coefficient and the original decision information to solve the MP-MADM problems. Finally, two MP-MADM cases are used to illustrate the effectiveness and practicability of the proposed method. Comparisons with previous research are also discussed.