At present, the local appearance-based texture descriptors in Facial Expression Recognition have limited accuracy due to the inability to encode the discriminative edges. The major cause is the presence of distorted and weak edges due to noise. Hence, this paper proposes new Expression Descriptor called as Weighted Edge Local Directional Pattern (WELDP) which can discriminate the weak and strong edges. Unlike the conventional local descriptors, WELDP searches for the support of neighbor pixels in the determination of Facial expression attributes such as Edges, Corners, Lines, and Curved Edges. WELDP encodes only Strong edge responses and discards weaker edge responses after extracting them through edge detection masks. This work adapted two masks for edge detection: they are Robinson Compass Mask and Kirsch Compass Mask. Moreover, the WELDP aims at code redundancy and encode each pixel only with seven bits (one sign bit and six directional bits). Then the WELDP image is described by a histogram and then processed through SVM (Support Vector Machine) for expression identification. From the simulation experiments, the proposed WELDP is found as better than several existing methods.