We describe the implementation of a simple technique to simulate core-level spectra within the Car-Parrinello plane-waves molecular dynamics framework. The x-ray absorption (XA) spectra are generated using the transition potential technique with the effect of the core hole included through a specifically developed pseudopotential for the core-excited atom. Despite the lack of 1s core orbitals in the pseudopotential treatment, the required transition moments are accurately calculated without reconstruction of the all-electron orbitals. The method is applied to the oxygen XA spectra of water in its various aggregation states, but it is transferable to any first-row element. The computed spectra are compared favorably with the results from all-electron cluster calculations, as well as with experimental data. The periodicity of the plane-wave technique improves the description of condensed phases. The molecular dynamics simulation enables in principle a proper treatment of thermal effects and dynamical averaging in complex systems.