Airborne light detection and ranging (LiDAR) has been recognized as a reliable and accurate measurement tool in forest volume estimation, urban scene reconstruction and land cover classification, where LiDAR data provide crucial and efficient features such as intensity, elevation and coordinates. Due to the complex urban environment, it is difficult to classify land cover accurately and quickly from remotely sensed data. Methods based on the Dempster–Shafer evidence theory (DS theory) offer a possible solution to this problem. However, the inconsistency in the correspondence between classification features and land cover attributes constrains the improvement of classification accuracy. Under the original DS evidence theory classification framework, we propose a novel method for constructing a basic probability assignment (BPA) function based on possibility distributions and apply it to airborne LiDAR land cover classification. The proposed approach begins with a feature classification subset selected by single-feature classification results. Secondly, the possibility distribution of the four features was established, and the uncertainty relationship between feature values and land cover attributes was obtained. Then, we selected suitable interval cut-off points and constructed a BPA function. Finally, DS evidence theory was used for land cover classification. LiDAR and its co-registration data acquired by Toposys Falcon II were used in the performance tests of the proposed method. The experimental results revealed that it can significantly improve the classification accuracy compared to the basic DS method.