Abstract We propose a new observing method for single-dish millimeter and submillimeter spectroscopy using a heterodyne receiver equipped with a frequency-modulating local oscillator (FMLO). Unlike conventional switching methods, which extract astronomical signals by subtracting the reference spectra of off-sources from those of on-sources, the FMLO method does not need to obtain any off-source spectra; rather, it estimates them from the on-source spectra themselves. The principle uses high-dump-rate (10 Hz) spectroscopy with radio frequency modulation achieved by fast sweeping of a local oscillator of a heterodyne receiver. Because sky emission (i.e., off-source) fluctuates as $1/f$ and is spectrally correlated, it can be estimated and subtracted from time series spectra (a timestream) by principal component analysis. Meanwhile, astronomical signals remain in the timestream since they are modulated to a higher time-frequency domain. The FMLO method therefore achieves (1) a remarkably high observation efficiency, (2) reduced spectral baseline wiggles, and (3) software-based sideband separation. We developed an FMLO system for the Nobeyama $45\:$m telescope and a data reduction procedure for it. Frequency modulation was realized by a tunable and programmable first local oscillator. With observations of Galactic sources, we demonstrate that the observation efficiency of the FMLO method is dramatically improved compared to conventional switching methods. Specifically, we find that the time to achieve the same noise level is reduced by a factor of 3.0 in single-pointed observations and by a factor of 1.2 in mapping observations. The FMLO method can be applied to observations of fainter ($∼$mK) spectral lines and larger ($∼$deg$^{2}$) mapping. It offers much more efficient and baseline-stable observations compared to conventional switching methods.