A two-sided matching decision method considering the matching aspirations is proposed to solve the intuitionistic fuzzy two-sided matching problem based on a novel ranking function. The related theories of the ranking function of intuitionistic fuzzy set are introduced. The intuitionistic fuzzy two-sided matching problem considering agents' matching aspirations is described. The decision method is given as follows. The preference of intuitionistic fuzzy sets is firstly transformed into the preference of ranking values according to the new ranking function. Based on the ranking value matrices, the matching aspiration matrix and the matching matrix, a multi-objective two-sided matching model considering the matching aspirations is developed. Considering the statuses of all agents on both sides are the same in most situations, the multi-objective model is converted into a single-objective model using the mean value method. The two-sided matching alternative is determined by model solution. An example analysis further explains the effectiveness of the proposed decision method.