A new, complete sample of 14,584 broad-line active galactic nuclei (AGNs) at z < 0.35 is presented, which are uncovered homogeneously from the complete database of galaxies and quasars observed spectroscopically in the Sloan Digital Sky Survey Seventh Data Release. The stellar continuum is properly removed for each spectrum with significant host absorption line features, and careful analyses of the emission line spectra, particularly in the H alpha and H beta wavebands, are carried out. The broad Balmer emission line, particularly H alpha, is used to indicate the presence of an AGN. The broad H alpha lines have luminosities in a range of 10(38.5) - 10(44.3) erg s(-1), and line widths (FWHMs) of 500-34,000 km s(-1). The virial black hole masses, estimated from the broad-line measurements, span a range of 10(5.1) - 10(10.3) M-circle dot, and the Eddington ratios vary from -3.3 to 1.3 in logarithmic scale. Other quantities such as multiwavelength photometric properties and flags denoting peculiar line profiles are also included in this catalog. We describe the construction of this catalog and briefly discuss its properties. The catalog is publicly available online. This homogeneously selected AGN catalog, along with the accurately measured spectral parameters, provides the most updated, largest AGN sample data, which will enable further comprehensive investigations of the properties of the AGN population in the low-redshift universe.