The massive penetration of renewable energy makes the solution of traditional unit commitment infeasible. The paper mainly studied the model with uncertain variable constraints. Firstly, the power balance constraint with uncertain variables is relaxed into an inequality constraint, and the inequality constraint, the reserve constraint and the transmission line constraint are transformed into a distributionally robust chance constraint model with ambiguity set based on the moment information and the two-sided model is used to deal with the transmission line constraints to improve reliability. In order to make the model traceable, the Bonferroni approximation is used to approximate the two-sided model and the unit commitment model is transformed into a mixed integer linear programming problem by linearization method. The conservativeness of the model is reduced by assuming that the distribution function in the ambiguity set is unimodal. Finally, case analysis of six-bus system and numerical results verified the validity of the proposed model.