We present a large catalog of optically selected galaxy clusters from the application of a new Gaussian Mixture Brightest Cluster Galaxy (GMBCG) algorithm to SDSS Data Release 7 data. The algorithm detects clusters by identifying the red-sequence plus brightest cluster galaxy (BCG) feature, which is unique for galaxy clusters and does not exist among field galaxies. Red-sequence clustering in color space is detected using an Error Corrected Gaussian Mixture Model. We run GMBCG on 8240 deg^2^ of photometric data from SDSS DR7 to assemble the largest ever optical galaxy cluster catalog, consisting of over 55,000 rich clusters across the redshift range from 0.1<z<0.55. We present Monte Carlo tests of completeness and purity and perform cross-matching with X-ray clusters and with the maxBCG sample at low redshift. These tests indicate high completeness and purity across the full redshift range for clusters with 15 or more members.