JPEG image compression algorithm is a widely used technique for image size reduction in edge and cloud computing settings. However, applying such lossy compression on images processed by deep neural networks can lead to significant accuracy degradation. Inspired by the curriculum learning paradigm, we propose a training approach called curriculum pre-training (CPT) for crowd counting on compressed images, which alleviates the drop in accuracy resulting from lossy compression. We verify the effectiveness of our approach by extensive experiments on three crowd counting datasets, two crowd counting DNN models and various levels of compression. The proposed training method is not overly sensitive to hyper-parameters, and reduces the error, particularly for heavily compressed images, by up to 19.70%.