Convolutional neural networks (CNNs) for biomedical image analysis are often of very large size, resulting in high memory requirement and high latency of operations. Searching for an acceptable compressed representation of the base CNN for a specific imaging application typically involves a series of time-consuming training/validation experiments to achieve a good compromise between network size and accuracy. To address this challenge, we propose CC-Net, a new image complexity-guided CNN compression scheme for biomedical image segmentation. Given a CNN model, CC-Net predicts the final accuracy of networks of different sizes based on the average image complexity computed from the training data. It then selects a multiplicative factor for producing a desired network with acceptable network accuracy and size. Experiments show that CC-Net is effective for generating compressed segmentation networks, retaining up to 95% of the base network segmentation accuracy and utilizing only 0.1% of trainable parameters of the full-sized networks in the best case.