Polarimetric synthetic aperture radar (PolSAR) images are widely used in disaster detection and military reconnaissance and so on. However, their interpretation faces some challenges, e.g., deficiency of labeled data, inadequate utilization of data information and so on. In this paper, a complex-valued generative adversarial network (GAN) is proposed for the first time to address these issues. The complex number form of model complies with the physical mechanism of PolSAR data and in favor of utilizing and retaining amplitude and phase information of PolSAR data. GAN architecture and semi-supervised learning are combined to handle deficiency of labeled data. GAN expands training data and semi-supervised learning is used to train network with generated, labeled and unlabeled data. Experimental results on two benchmark data sets show that our model outperforms existing state-of-the-art models, especially for conditions with fewer labeled data.