A two-sided matching method considering regret aversion psychological behavior of agents is proposed to solve the twosided matching problems with multi-form uncertain preference information based on the regret theory. Firstly, this paper renders uncertain preference ordinal and uncertain linguistic information of two group agents into utility values. Secondly, the regret values are calculated of agents based on regret theory, then the perception utility values of each agent is gained. Furthermore, the twosided matching model is constructed. Finally, an example of cloud manufacturing service outsourcing matching problem is given to demonstrate the effectiveness of the two-sided matching method.