We investigate the vortex structure in chiral p-wave superconductors by the Bogoliubov-de Gennes theory on a tight-binding model. We calculate the spatial structure of the pair potential and electronic state around a vortex, including the anisotropy of the Fermi surface and superconducting gap structure. The differences of the vortex structure between sin px+i sin py-wave and sin px-i sin py-wave superconductors are clarified in the vortex lattice state. We also discuss the winding ∓3 case of the sin(px+py)±i sin(-px+py)-wave superconductivity.