Feature extraction is a very important step for polarimetric synthetic aperture radar (PolSAR) image classification. Many dimensionality reduction (DR) methods have been employed to extract features for supervised PolSAR image classification. However, these DR-based feature extraction methods only consider each single pixel independentlyand thus fail to take into account the spatial relationship of the neighboring pixels, so their performance may not be satisfactory. To address this issue, we introduce a novel tensor local discriminant embedding (TLDE) method for feature extraction for supervised PolSAR image classification. The proposed method combines the spatial and polarimetric information of each pixel by characterizing the pixel with the patch centered at this pixel. Then each pixel is represented as a third-order tensor of which the first two modes indicate the spatial information of the patch (i.e., the row and the column of the patch) and the third mode denotes the polarimetric information of the patch. Based on the label information of samples and the redundance of the spatial and polarimetric information, a supervised tensor-based DR technique, called TLDE, is introduced to find three projections which project each pixel, that is, the third-order tensor into the low-dimensional feature. Finally, classification is completed based on the extracted features using the nearest neighbor classifier and the support vector machine classifier. The proposed method is evaluated on two real PolSAR data sets and the simulated PolSAR data sets with various number of looks. The experimental results demonstrate that the proposed method not only improves the classification accuracy greatly but also alleviates the influence of speckle noise on classification.