A collection of 18 Iberian earthquakes, felt with epicentral intensity I0 ≥ VI (MSK) in the Iberian Peninsula during the period 1923–1961, just before the introduction of the WWSSN stations in 1962, have been investigated through digital reconstruction of old seismograms recorded in four Spanish seismological observatories: Alicante, Almería, Ebro, and Toledo. Spectral analysis of the seismic waves recorded at the different stations has been performed and the seismic moment of the early instrumentally recorded earthquakes considered has been calculated according to the model of Brune (1970) and applying corrections by instrumental response, anelastic attenuation, free surface, and radiation pattern. A seismic moment-magnitude relation has been obtained, and the result has been compared with other regressions obtained for different seismo-active regions in Spain and in the world. The moment magnitudes of the earthquakes considered have been calculated according to the scale of Kanamori (1977) and Hanks and Kanamori (1979). Finally, a magnitude correction for the conversion of surface wave magnitude to moment magnitude has been proposed: M = 0.96 M(A/T) – 0.36. This conversion should be considered valid for the 4.0–6.0 surface-wave magnitude interval, which spans well the characteristic range for the moderate seismic activity in the Iberian Peninsula.