An effective method is proposed to solve the group decision-making problems with uncertain multiplicative linguistic information. First, to compare two uncertain multiplicative linguistic variables, a possibility degree formula is introduced in accordance with the operation laws. Some desirable properties of possibility degree are provided. Then, the uncertain multiplicative linguistic hybrid weighted geometric averaging (ULHWG) operator is developed to aggregate uncertain multiplicative linguistic variables into an overall preference value. Thus, a comprehensive algorithm for linguistic group decision-making is proposed based on the deviation measure and the ULHWG operator. Finally, a numerical example is provided to illustrate the practicality and validity of the proposed method.