Terahertz imaging technology faces limitations related to the performance of terahertz radiation sources and detectors, necessitating improvements in detail resolution, imaging speed, and noise reduction. To address these challenges, this paper proposes a method for enhancing terahertz imaging resolution based on space curve filling. The backbone network utilizes the Vision Transformer (ViT) architecture, which extracts features from terahertz images through its attention mechanism. Subsequently, a Hilbert space curve is constructed to facilitate the reconstruction of the image by filling the feature map with the curve. Lightweight one-dimensional convolution is employed to process the reconstructed image features, followed by an inverse transformation to restore the spatial structure of the image. Finally, upsampling is achieved through pixel reorganization, resulting in a terahertz super-resolution image with distinct contours and precise details. Experimental results demonstrate that, compared to the traditional ViT structure, the proposed method achieves an improvement of 0.81 dB in peak signal-to-noise ratio (PSNR) and 0.0074 in structural similarity index (SSIM). Additionally, the method effectively mitigates the impact of noise on image texture, yielding a more realistic terahertz super-resolution image. These findings validate the feasibility of terahertz imaging super-resolution technology and its potential to enhance image quality and detail restoration.