High-resolution scanning superconducting quantum interference device (SQUID) microscopy was used to study the flux quantization phenomenon in multiply-connected anisotropic high-Tc NdBa2Cu3O7-d single crystalline thin films. The spatial distribution of internal flux in a hole was found to be non-uniform and changed drastically for applied small fields. With increased fields above 10uT, a local magnetic dipole flux developed inside the hole, in contrast to an isotropic Nb superconductor. The total net flux trapped in a hole was kept to be constant for larger holes, but the abrupt transition of flux quantization state was observed for smaller holes. The possible explanation is given based on the anisotropic dx2-y2-wave order parameter of high-Tc superconductors.