This paper discusses the electronic structure in the vortex core in relation to the pinning potential under the influence of the pseudo-gap which opens in the normal state in the high-temperature superconductor (HTS). It is argued that the condensation energy may be significantly reduced in the under-doped regime where the pseudo-gap becomes pronounced and hence it should be deeply related with the small pinning force in this regime. The empirical scaling laws observed for the vortex behaviors in the mixed state phase diagram are also discussed in terms of the condensation energy and the anisotropy factor. ©1999 American Institute of Physics.