Deep learning (DL) based image processing methods have been successfully applied to low-dose x-ray images based on the assumption that the feature distribution of the training data is consistent with that of the test data. However, low-dose computed tomography (LDCT) images from different commercial scanners may contain different amounts and types of image noise, violating this assumption. Moreover, in the application of DL based image processing methods to LDCT, the feature distributions of LDCT images from simulation and clinical CT examination can be quite different. Therefore, the network models trained with simulated image data or LDCT images from one specific scanner may not work well for another CT scanner and image processing task. To solve such domain adaptation problem, in this study, a novel generative adversarial network (GAN) with noise encoding transfer learning (NETL), or GAN-NETL, is proposed to generate a paired dataset with a different noise style. Specifically, we proposed a method to perform noise encoding operator and incorporate it into the generator to extract a noise style. Meanwhile, with a transfer learning (TL) approach, the image noise encoding operator transformed the noise type of the source domain to that of the target domain for realistic noise generation. One public and two private datasets are used to evaluate the proposed method. Experiment results demonstrated the feasibility and effectiveness of our proposed GAN-NETL model in LDCT image synthesis. In addition, we conduct additional image denoising study using the synthesized clinical LDCT data, which verified the merit of the proposed synthesis in improving the performance of the DL based LDCT processing method.