A vetoed multi-attribute grey target decision method is proposed and demonstrated with a practical case study. Firstly, a classical multi-objective grey target decision model is introduced, then a veto function is defined with a hesitant region, which can accommodate some vagueness in the decision maker’s specification of this level to reject a scheme. Secondly, a vetoed synthetic effect measure matrix is obtained based on the veto function and the uniform effect measure. Finally, the proposed model is applied to a supplier selection problem for official vehicles. The decision method proposed in this study, which is expressed by the vetoed synthetic effect measure, is reasonable and useful in decision-making practice.