We perform large-scale numerical calculations self-consistently solving the Bogoliubov-de Gennes (BdG) equations in the magnetic field together with random impurities to directly demonstrate the typical quasi-particle interference (QPI) in the presence of vortices as observed by scanning tunneling microscopy/spectroscopy experiments in unconventional superconductors. The calculations reveal that vortex itself never works as a scatter causing the QPI pattern but vortex core containing impurity brings about the enhancement of the sign-preserving QPI peaks. Its origin is Andreev bound-states distorted by impurity, and all the measurement findings are consistently explained by the scenario based on the numerical results.