Abstract We developed a new technique for identifying active galactic nuclei (AGNs) and studied the nature of low-luminosity AGNs in the Sloan Digital Sky Survey. This is the former part of a series of papers. We develop a new, sensitive method of identifying AGNs in this paper. The emission-line luminosity in a spectrum is the sum of a star-formation component and an AGN component (if present). We demonstrate that an accurate estimate of the star-formation component can be achieved by fitting model spectra, generated with a recent stellar population synthesis code, to a continuum spectrum. By comparing the observed total line luminosity with that attributed to star formation, we can tell whether a galaxy hosts an AGN or not. We compare our method with the commonly used emission-line diagnostics proposed by Baldwin, Phillips, and Terlevich (1981, PASP, 93, 5; hereafter BPT). By this method, we classify 85% of the strong emission-line objects in the same star-formation/AGN as BPT. One unique feature of our method is its sensitivity; it is applicable to nearly twice as many objects as BPT. We further make a comparison between our method and the BPT diagnostics using stacked spectra and selections in X-ray and radio wavelengths. We show that it is overall a sensitive method of identifying AGNs, while our method suffers from incompleteness and contamination as any AGN identification method does so. We emphasize that our method can be applied at high redshifts (up to ${z}$$\sim$ 1.7 with red-sensitive optical spectrograph) without making any a priori assumptions about the host-galaxy properties. Another unique feature is that it allows us to subtract the emission-line luminosity due to star formation, and to extract the intrinsic AGN luminosity.