Polarimetric synthetic aperture radar (PolSAR) as a typical multi-channel sensor can obtain refined geometrical and geophysical information. In the PolSAR land cover classification task, feature extraction is regarded as a critical step for the final classification. It can employ multi-modal features from the original scattering data, polarimetric target decomposition, and other transformation space. Then, how to efficiently combine multi-modal polarimetric information and extract discriminant features is an important challenge for PolSAR image processing. Graph embedding methods have become a significant technique to deal with feature extraction and dimensionality reduction (DR) problems in recent years. It provides a unified linearization framework in machine learning and other pattern recognition tasks. In this article, an extended tensor embedding framework is introduced to extract the intrinsic features for PolSAR land cover classification. First, each pixel is represented by a feature cube that is constructed by groups of polarimetric scattering signals and target decomposition features in a fixed size patch. Second, an intrinsic matrix is constructed to describe the original geometrical and statistical properties of the samples, and a penalty matrix is designed to represent some constraints. Third, the vector-based algorithms are transformed into tensor space in an unified framework and based on the pair of matrices to obtain the projection matrices in each mode by an iterative optimization process. The effectiveness of the proposed methods is demonstrated on three RADARSAT2 data sets covering the regions of Xi'an, San Francisco, and Flevoland, respectively. The visualization and quantification results show that the proposed method has superiority in land cover classification.