A spectral analysis algorithm based on the combination of Hilbert transform (HT) and power spectrum estimation has been proposed, and the terahertz reflection time domain waveform was processed. At the same time, the algorithm was applied to terahertz time domain spectroscopy imaging, defect thickness was correlated with image gray level, and the thickness, position and shape of defects in glass fiber laminate can be detected by imaging simultaneously. The experimental results show that when the multi-signal classification (MUSIC) spectrum estimation and auto regressive (AR) spectrum estimation are combined with Hilbert transform, the reflected pulses between upper and lower surfaces of defect with thickness of 0.08 mm can be successfully distinguished, the time resolution of reflected pulses is higher than 0.5 ps, and the detection error of defect thickness is no more than 0.03 mm.