As the third installment in a series systematically searching dual active galactic nuclei (AGN) among merging galaxies, we present the results of 20 dual AGNs found by using the SDSS fiber spectra. To reduce the flux contamination from both the fiber aperture and seeing effects, the angular separation of two cores in our merging galaxy pairs sample is restricted at least larger than 3 ''. By careful analysis of the emission lines, 20 dual AGNs are identified from 61 merging galaxies with their two cores both observed by the SDSS spectroscopic surveys. 15 of them are identified for the first time. The identification efficiency is about 32.79% (20/61), comparable to our former results (16 dual AGNs identified from 41 merging galaxies) based on the long-slit spectroscopy. Interestingly, two of the 20 dual AGNs show two prominent cores in radio images and their radio powers show they as the radio-excess AGNs. So far, 31 dual AGNs are found by our project and this is the current largest dual AGN sample, ever constructed with a consistent approach. This sample, together with more candidates from ongoing observations, is of vital importance to study the AGN physics and the coevolution between the supermassive black holes and their host galaxies.