In this paper, we propose a novel method to measure the free spectral range (FSR) of a Fabry-Perot cavity (FPC) using single-frequency modulation (FM) with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a cosine-wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FPC. The transmission light from the FPC is observed and converted to an RF signal by a highs-peed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier (LIA) by referring to the oscillator. We theoretically and experimentally demonstrate that the LIA signal become null with a steep slope, when the modulation frequency equals the FSR under the condition that the carrier frequency is slightly detuned from the resonance of the FPC. The experimental results show that the proposed method has the capability to determine the FSR by the null method with a small measurement uncertainty.