We apply the maximum entropy method to extract the spectral functions for pseudoscalar and vector mesons from hadron correlators previously calculated at four different lattice spacings in quenched QCD with the Wilson quark action. We determine masses and decay constants for the ground and excited states of the pseudoscalar and vector channels from the position and area of peaks in the spectral functions. We obtain the results mp1=660(590) MeV and mr 1=1540(570) MeV for the first excited state masses, in the continuum limit of quenched QCD. We also find unphysical states that have an infinite mass in the continuum limit, and argue that they are bound states of two doublers of the Wilson quark action. If the interpretation is correct, this is the first time that the state of doublers has been identified in lattice QCD numerical simulations.