The super-resolution reconstruction for seismic images obtained by multistep processing of field data is essential due to the noise contamination, sparse geometry, and low dominant frequency of events, which impairs the subsequent seismic interpretation. Deep learning-based methods show strong potential in super-resolution through supervised learning. Generative adversarial networks (GANs) have shown capability in super-resolution of different kinds of images; however, it is limited in enhancing the detailed geological structures of seismic images that are fatal for interpretation. To address this issue, we propose a super-resolution hybrid bilateral attention GAN (SHBGAN) to improve the recovery of weak signals and the reconstruction of geological structures. Specifically, the generator employs hybrid and bilateral attention modules (BAMs) to enhance the capture ability of global and local features. Meanwhile, we use dilated convolutional layers instead of batch normalization (BN) layers in the residual block to improve the generalization ability of the trained model. Meanwhile, the discriminator employs global average pooling and convolutional layers to score the authenticity of seismic images rather than the probability to enhance the stability of training. In addition, we add the mean structural similarity (MSSIM) term to the loss function of generator to improve the perception quality of predictions. The numerical tests on both synthetic and field data show that SHBGAN is more effective than competing methods in recovering weak signals and reconstructing subtle faults.