We present the first catalog of 67 strong galaxy-galaxy lens candidates discovered in the 1.64deg^2^ Hubble Space Telescope COSMOS survey. Twenty of these systems display multiple images or strongly curved large arcs. Our initial search is performed by visual inspection of the data and is restricted, for practical considerations, to massive early-type lens galaxies with arcs found at radii smaller than ~5". Simple mass models are constructed for the best lens candidates, and our results are compared to the strong lensing catalogs of the SLACS survey and the CASTLES database. These new strong galaxy-galaxy lensing systems constitute a valuable sample to study the mass distribution of early-type galaxies and their associated dark matter halos.