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 DES 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 20000 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.