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 p(x)+i sin p(y)-wave and sin p(x)-i sin p(y)-wave superconductors are clarified in the vortex lattice state. We also discuss the winding -/+3 case of the sin(p(x)+p(y))=i sin(-p(x)+p(y))-wave superconductivity.