In this paper, we focus on developing a novel method to extract sea ice cover (i.e., discrimination/classification of sea ice and open water) using Sentinel-1 (S1) cross-polarization (vertical-horizontal, VH or horizontal-vertical, HV) data in extra wide (EW) swath mode based on the machine learning algorithm support vector machine (SVM). The classification basis includes the S1 radar backscatter coefficients and texture features that are calculated from S1 data using the gray level co-occurrence matrix (GLCM). Different from previous methods where appropriate samples are manually selected to train the SVM to classify sea ice and open water, we proposed a method of unsupervised generation of the training samples based on two GLCM texture features, i.e. entropy and homogeneity, that have contrasting characteristics on sea ice and open water. We eliminate the most uncertainty of selecting training samples in machine learning and achieve automatic classification of sea ice and open water by using S1 EW data. The comparison shows good agreement between the SAR-derived sea ice cover using the proposed method and a visual inspection, of which the accuracy reaches approximately 90% - 95% based on a few cases. Besides this, compared with the analyzed sea ice cover data Ice Mapping System (IMS) based on 728 S1 EW images, the accuracy of extracted sea ice cover by using S1 data is more than 80%.