We investigate the change of the vortex structure in the presence of the induced stripe or checkerboard pattern modulation of the incommensurate spin density wave (SDW) and charge density wave (CDW) around the vortex core. The order parameter and the quasiparticle structure in the vortex lattice state are calculated by Bogoliubov-de Gennes theory on a two-dimensional Hubbard model with nearest-neighbor site pairing interaction. By the induced SDW and CDW, low-energy excitations around the vortex core are suppressed, producing "empty core" structure, as observed by the scanning tunneling microscopy. In the relation to these quasiparticle structures, we discuss the site-selective nuclear spin relaxation time T, and thermal conductivity in the vortex state. (c) 2005 Elsevier B.V. All rights reserved.