We search Dark Energy Survey (DES) Year 3 imaging for galaxy-galaxy strong gravitational lenses using convolutional neural networks, extending previous work with new training sets and covering a wider range of redshifts and colors. We train two neural networks using images of simulated lenses, then use them to score postage stamp images of 7.9 million sources from the Dark Energy Survey chosen to have plausible lens colors based on simulations. We examine 1175 of the highest-scored candidates and identify 152 probable or definite lenses. Examining an additional 20,000 images with lower scores, we identify a further 247 probable or definite candidates. After including 86 candidates discovered in earlier searches using neural networks and 26 candidates discovered through visual inspection of blue-near-red objects in the DES catalog, we present a catalog of 511 lens candidates.