Magnetic Resonance Imaging (MRI) is one of the most commonly used modalities in medical imaging, and one of the main limitations is its slow scanning and reconstruction speed. Recently, deep learning used for compressed sensing (CS) methods have been proposed to accelerate the acquisition by undersampling in the K-space and reconstruct images with neural networks. However, there are still some challenges remained: First, directly training networks based on L1/L2 distance to the target fully sampled images may lead to fuzzy reconstruction images because L1/L2 loss only enforces the overall image or patch similarity, but does not consider the local details such as anatomical sharpness. Second, Generative Adversarial Networks (GAN) can partially solve this problem. The undersampling image gets the latent space through the encoder, and the image is reconstructed by the decoder based on GAN loss, but it may generate unrealistic details by lacking of constraints in K-space domain. Third, most of the networks after training are fixed and have limited adaptation capability in the inference time, and the patient-specific information cannot be effectively used. To resolve these challenges, we proposed a new compressed sensing GAN reconstruction method, and there are two main contributions: (1) We proposed a encoder-decoder structure, which guided GAN optimization strategy data-consistency in latent space to improve the reconstruction quality such as preserving more local details and improving the anatomical sharpness while constraining GAN to follow the data distribution in the K-space to prevent the unrealistic details. (2) An online update strategy is used to find the best representation in the latent space for the underlying patient, and the reconstruct result can be further improved by incorporating the patient-specific information. Extensive experimental results show the effectiveness of our method.