We present a new decision making model with distance measures by using linguistic aggregation operators. We introduce a new aggregation operator called the linguistic ordered weighted averaging distance (LOWAD) operator. This aggregation operator provides a parameterized family of linguistic aggregation operators that includes the maximum distance, the minimum distance, the linguistic normalized Hamming distance and the linguistic weighted Hamming distance, among others. We study some of its main properties and different families of LOWAD operators such as the median-LOWAD, the Olympic-LOWAD, the S-LOWAD and the centered-LOWAD. We also develop an application of the new approach in a decision making problem concerning human resource management.