We present an efficient proposal to realize quantum nondestructive determination (QNDD) of unknown single-qubit states in two types of low-Q cavities, i.e., single-sided and double-sided cavity QED systems. In the dispersive regime, we demonstrate that the QNDD of single-qubit states can be realized by detecting qubit-state-dependent phase shifts (QSDPSs) of the reflected or transmitted photons from the cavity in the single-photon input-output process. Our proposal could be straightforwardly extended to the case of multiple-qubit states. Furthermore, the experimental feasibility of our proposal is also analyzed in experimentally-demonstrated circuit QED systems. The distinct feature of our proposal is that our proposal works in the dispersive regime of low-Q cavities and it is robust to both cavity decay and atomic spontaneous emission.