Summary: We generalize linguistic evaluation values and their weights in group decision-making (GDM) problems based on unbalanced linguistic terms. The GDM problems include two types of weights: belief degrees of linguistic evaluation values and experts’ weights. Due to the time pressure and conflict of multi-source of information, etc., experts may have various evaluations values on alternatives. The belief degree is used to represent the confidence level of the values. The experts’ weight is used to represent the differences among experts’ importance which caused by experts’ experience or knowledge distinction. We propose the weighted unbalanced linguistic aggregation operators to synthesize linguistic evaluation value, belief degree and experts’ weights. Some desired properties of the operator are then studied, these properties show that the operator extends the linguistic weighted averaging operator (LWA) and the linguistic ordered weighted averaging (LOWA) operator. Finally, an illustrative example of human resource performance appraisal based on the linguistic aggregation operator is provided.