The performance of radiation sources and detectors currently limits terahertz imaging technology, which still requires further improvement in terms of detail resolution, imaging speed, and noise suppression. This paper proposes a terahertz image super-resolution algorithm based on spatial curve filling. The ViT (Vision Transformer) structure backbone network is utilized to extract terahertz image features through an attention mechanism. A Hilbert spatial curve is constructed to reconstruct the image according to the feature map using the curve filling method. Lightweight one-dimensional convolution processing is used for reconstructing image features, while inverse transformation of reconstructed maps restores the image's spatial structure. Finally, pixel reorganization enables up sampling to obtain an output image with enhanced object contour and details. Experimental results show that compared with conventional ViT structures, this proposed method improves Peak Signal-to-Noise Ratio (PSNR) by 0.81 dB and Structural Similarity Index (SSIM) by 0.007 4, which effectively inhibits the noise influence on texture and significantly improves the resolution and image quality.