A robust fake satellite image detection method, called Geo-DefakeHop, is proposed in this work. Geo-DefakeHop is developed based on the parallel subspace learning (PSL) methodology. PSL maps the input image space into several feature subspaces using multiple filter banks. By exploring response differences of different channels between real and fake images for a filter bank, Geo-DefakeHop learns the most discriminant channels and uses their soft decision scores as features. Then, Geo-DefakeHop selects a few discriminant features from each filter bank and ensemble them to make a final binary decision. Geo-DefakeHop offers a light-weight high-performance solution to fake satellite images detection. Its model size is analyzed, which ranges from 0.8 to 62K parameters. Furthermore, it is shown by experimental results that it achieves an F1-score higher than 95\% under various common image manipulations such as resizing, compression and noise corruption.