The two-sided matching problem has always been concerned by the scholars in the fields of economic management and so on． A novel decision method is proposed to solve the two-sided matching problem based on incomplete ordinal number information from the point of view of complete two-sided matching． In this paper，the two-sided matching problem is firstly described，and the concept of complete two-sided matching is introduced． Then，the existence of complete two-sided matching is investigated． Furthermore，the methods for two-sided matching in the condition that complete two-sided matching exists and doesn’t exist are presented respectively． On this basis，the algorithm for solving the two-sided matching problem based on incomplete ordinal numbers is developed． The result of complete two-sided matching can be obtained by using the algorithm．The example analysis illustrates the feasibility and validity of the proposed method．