We report the development of the frequency-modulation (FM) method for measuring electron spin resonance (ESR) absorption in the 210- to 420GHz frequency range. We demonstrate that using a high-frequency ESR spectrometer without resonating microwave components enables us to overcome technical difficulties associated with the FM method due to nonlinear microwave-elements, without sacrificing spectrometer performance. FM was achieved by modulating the reference oscillator of a 13GHz Phase-Locked Dielectric Resonator Oscillator, and amplifying and frequency-multiplying the resulting millimeter-wave radiation up to 210, 315 and 420GHz. ESR spectra were obtained in reflection mode by a lock-in detection at the fundamental modulation frequency, and also at the second and third harmonic. Sensitivity of the setup was verified by conduction electron spin resonance measurement in KC60.