Terahertz time-domain spectral images of polymer 3D printed samples with internal defects are obtained using terahertz time-domain spectral imaging technique. The preliminary results show that the defects in the sample and the materials have different absorption and reflection of terahertz waves. The external defects of 3D printed materials can be characterized directly by terahertz spectroscopy imaging. However, for the internal defects of the sample,the results of terahertz spectroscopy imaging need to be further optimized. Further study shows that being optimized by Gaussian noise addition, superposition fusion, least squares denoising and other algorithms, clear terahertz time-domain spectral images of internal defects can be obtained. Therefore, it is shown that the internal defects of organic polymer 3D printing materials can be characterized by terahertz time-domain spectral imaging technique combined with optimization algorithms.