Owing to the fuzziness and hesitation of people in evaluating process, it is often difficult to give numerical preference information directly. Probabilistic linguistic term sets (PLTSs) is an effective tool to deal with the fuzziness and hesitation of evaluation information, besides, considering the different risk preferences of matching subjects and the competitive relationship between them, a probabilistic linguistic two-sided matching method based on competitive effect is proposed. Firstly, a new distance measure of PLTSs is proposed. Secondly, according to prospect theory construct the comprehensive prospect matrix of matching subjects and further using min-max normalization method convert the comprehensive prospect matrix into satisfaction matrix. Thirdly, a competitive relationship network is proposed to describe the competitive relationship between subjects, and two-stages of competition: macro competition and micro competition are defined. Then, the calculation formula of competitive correlation strength is proposed and transformed into satisfaction of subjects. Based on the maximization of satisfaction, a multi-objective two-sided matching optimization model considering competitive effect is established, the satisfactory matching results are obtained by solving this model. Finally, an example and some comparative studies are presented to demonstrate the effectiveness and practicability of this method.