We numerically study the quantum oscillations in superconducting vortex-mixed states with d-wave pairing. We show that in the parameter range of an underdoped cuprate superconductor, the commonly held assumption that the period is given by the underlying Fermi-surface area using the Onsager relation becomes invalid. Using this result, we conclude that the interpretation of the recent experimental data on YBCO as a signal of an underlying Fermi surface with four hole pockets created by a (π,π) folding cannot be ruled out.National Science Foundation