Deep learning (DL) has shown outstanding performances in many fields, including remote sensing (RS). DL is turning into an essential tool for the RS research community. Recently, many cloud platforms have been developed to provide access to large-scale computing capacity, consequently permitting the usage of DL architectures as a service. However, this opened the door to new challenges associated with the privacy and security of data. The RS data used to train the DL algorithms have several privacy requirements. Some of them need a high level of confidentiality, such as satellite images related to public security with high spatial resolutions. Moreover, satellite images are usually protected by copyright, and the owner may strictly refuse to share them. Therefore, privacy-preserving deep learning (PPDL) techniques are a possible solution to this problem. PPDL enables training DL on encrypted data without revealing the original plaintext. This study proposes a hybrid PPDL approach for object classification for very-high-resolution satellite images. The proposed encryption scheme combines Paillier homomorphic encryption (PHE) and somewhat homomorphic encryption (SHE). This combination aims to enhance the encryption of satellite images while ensuring a good runtime and high object classification accuracy. The method proposed to encrypt images is maintained through the public keys of PHE and SHE. Experiments were conducted on real-world high-resolution satellite images acquired using the SPOT6 and SPOT7 satellites. Four different CNN architectures were considered, namely ResNet50, InceptionV3, DenseNet169, and MobileNetV2. The results showed that the loss in classification accuracy after applying the proposed encryption algorithm ranges from 2% to 3.5%, with the best validation accuracy on the encrypted dataset reaching 92%.