Image classification plays an important role in remote sensing. Earth observation (EO) has inevitably arrived in the big data era, but the high requirement on computation power has already become a bottleneck for analyzing large amounts of remote sensing data with sophisticated machine learning models. Exploiting quantum computing might contribute to a solution to tackle this challenge by leveraging quantum properties. This article introduces a hybrid quantum-classical convolutional neural network (QC-CNN) that applies quantum computing to effectively extract high-level critical features from EO data for classification purposes. Besides that, the adoption of the amplitude encoding technique reduces the required quantum bit resources. The complexity analysis indicates that the proposed model can accelerate the convolutional operation in comparison with its classical counterpart. The model's performance is evaluated with different EO benchmarks, including Overhead-MNIST, So2Sat LCZ42, PatternNet, RSI-CB256, and NaSC-TG2, through the TensorFlow Quantum platform, and it can achieve better performance than its classical counterpart and have higher generalizability, which verifies the validity of the QC-CNN model on EO data classification tasks.