Recently, much attention has been paid to double-peaked narrow emission-line (NEL) galaxies, some of which are suggested to be related to merging galaxies. We make a systematic search to build the largest sample of these sources from Data Release 7 of the Sloan Digital Sky Survey (SDSS). With reasonable criteria for fluxes, FWHMs of the emission lines, and separations of the peaks, we select 3030 double-peaked NEL galaxies. In light of the existence of broad Balmer lines and the locations of the two components of double-peaked NELs distinguished by the Kauffmann et al. (2003MNRAS.346.1055K) criteria in the Baldwin-Phillips-Terlevich diagram, we find that there are 81 Type I active galactic nuclei (AGNs), 837 double Type II AGNs (2-Type II), 708 galaxies with double star-forming components (2-SF), 400 with mixed star-forming and Type II AGN components (Type II + SF), and 1004 unknown-type objects. As a by-product, a sample of galaxies (12582) with asymmetric or top-flat profiles of emission lines is established. After visually inspecting the SDSS images of the two samples, we find 54 galaxies with dual cores.