Facial expressions contain a lot of information about the feelings of a human. It plays an important role in humancomputer interaction. In this paper, entropy based feature selection method applied to 3D facial feature distances is presented for a facial expression recognition system classifying the expressions into 6 basic classes based on 3-Dimensional (3D) face geometry. Our previous work on entropy based feature selection has been improved by employing 3D feature distances between the 83 points on the face as facial features. 3D distances are more robust to rotations of the face and involve more accurate information than 3D feature positions that are used in our previous work. Entropy is applied in order to rank the feature distances for feature selection. The system is tested on BU-3DFE database in person independent manner and provides encouraging recognition rates.