A new experimental method for the high-resolution measurement of photoabsorption cross sections has been developed. The energy resolution of about 0.1% is achieved by measuring the transmitted photons from a target with a high-resolution high-energy photon spectrometer. The method is applied to the measurement of the photoabsorption cross section of 18O in the giant resonance region. Significant fine structure of the resonance is observed. © 1998 The American Physical Society.