The successful use of picosecond-pulse free-electron-laser (FEL) radiation for the continuous-wave terahertz-range electron spin resonance (ESR) spectroscopy has been demonstrated. The combination of two linac-based FELs (covering the wavelength range of 4–250 μm) with pulsed magnetic fields up to 70 T allows for multifrequency ESR spectroscopy in a frequency range of 1.2–75 THz with a spectral resolution better than 1%. The performance of the spectrometer is illustrated with ESR spectra obtained in the 2,2-diphenyl-1-picrylhydrazyl and the low-dimensional organic material (C6H9N2)CuCl3.