The two-sided matching problem has always been one of the hot issues discussed in the fields of economic management and so on． In the two-sided matching problems with complete preference ordinal information，it is more significant to consider the highest acceptable preference ordinal of two-sided agents．However，this kind of two-sided matching problem has not yet received great attention．Hence，a strict two-sided matching method is proposed．In this paper，the related concept on two-sided matching is firstly introduced，and then the two-sided matching problem with the highest acceptable preference ordinal based on complete preference ordinal information is described. In order to solve the problem，the concept and existence theory of strict two-sided matching is given．Considering the satisfaction degree and the lowest acceptable satisfaction degree of two-sided agents，a multi-objective optimization model is developed． By using linear weighted method，the multi-objective optimization model is converted into a single objective model．The matching result is obtained by solving the model．Finally，an illustrative example of two-sided matching between venture investors and venture businesses is given to illustrate the feasibility and validity of the proposed method．