Terahertz (THz) imaging has been applied successfully in numerous applications, from medical imaging to industrial non-destructive detection. However, low resolution has always been a problem due to its long wavelength. A convolution neural network (CNN) is quite effective at improving the resolution of images in optics, in which real numbers are manipulated corresponding to measured intensity. Compared to optics, it is quite feasible to gain both the amplitude and phase information in THz imaging. In this Letter, we have extended the CNN from a real number domain to a complex number domain based on the wave nature of THz light. To the best of our knowledge, this is the first time that such a complex convolution neural network (CCNN) has been shown to be successful in THz imaging. We have proved that resolution can be 0.4 times of the beam size via this approach, and half a wavelength resolution can be obtained easily. Compared to the CNN, the CCNN generates an extra 27.8% increase in terms of contrast, implying a better image. Phase information can be recovered well, which is impossible for the CNN. Although the network is trained by the MNIST dataset, it is quite powerful for image reconstruction. Again, the CCNN outperforms the CNN in terms of generalization capability. We believe such an approach can help to overcome the lower-resolution bottleneck in THz imaging, and it can release the requirement of critical optical components and extensive fine-tuning in systems. THz biomedical imaging, non-destructive testing (NDT), and a lot of imaging applications can benefit from this approach.