With respect to the two-sided matching problem, where the agents' preferences are in the format of two-granularity uncertain and incomplete linguistic terms, a matching method is presented. Some definitions on uncertain linguistic term and 2-tuple are firstly given. The two-sided matching problem with two-granularity uncertain and incomplete linguistic terms is described. Then, uncertain and incomplete linguistic term matrixes are transformed into 2tuple matrixes. Furthermore, a multi-objective optimization model is developed by using the extended 2-tuple weighted average. By using the 2-tuple arithmetic mean, the normalization method and the linear weighted method, the multi-objective optimization model can be converted into a single-objective optimization model. By solving the optimization model, the matching alternative can be obtained. A matching example illustrates the feasibility and effectiveness of this method.