The wavelet stretch effects in pre-stack migration, which is similar to that of NMO stretch, distort the frequency spectrums and taper the high-frequency components at far offsets. The long-offset migrated results in conventional migration methods are muted, resulting in a loss of effective information about the subsurface investigation. Only short-offset data are used to obtain a high-resolution stacked image. However, long-offsets that correspond to high-incident-angle data are critical to velocity inversion and amplitude versus offset (AVO) analysis when estimating lithology and fluid product. Furthermore, attenuation of seismic waves due to the anelasticity of the subsurface medium will cause dissipation of seismic energy and loss of high frequencies, thus broadening the propagating wavelet and degrading the resolution of imaging. Both the wavelet stretch and the absorption will taper the high-frequency components. We developed a wavelet stretch correction and absorption compensation scheme during the migration process by shrinking the wavelet when applying the imaging condition, which matches the stretch effect caused by migration. The correction factor is derived based on the incidence angle associated with many factors. Moreover, the de-absorption pre-stack time migration (QPSTM) is implemented on the effective Q model that makes the Q modelling become easier. Both the application of synthetic and real data examples demonstrate that the proposed anti-stretch QPSTM can be particularly useful recovering the high-frequency components caused by anelasticity and wavelet stretch, and obtain higher-resolution images.