We search Dark Energy Survey (DES) Year 3 imaging data for galaxy-galaxy strong gravitational lenses using convolutional neural networks. We generate 250 000 simulated lenses at redshifts > 0.8 from which we create a data set for training the neural networks with realistic seeing, sky and shot noise. Using the simulations as a guide, we build a catalogue of 1.1 million DES sources with 1.8 < g − i < 5, 0.6 < g − r < 3, r mag > 19, g mag > 20, and i mag > 18.2. We train two ensembles of neural networks on training sets consisting of simulated lenses, simulated non-lenses, and real sources. We use the neural networks to score images of each of the sources in our catalogue with a value from 0 to 1, and select those with scores greater than a chosen threshold for visual inspection, resulting in a candidate set of 7301 galaxies. During visual inspection, we rate 84 as 'probably' or 'definitely' lenses. Four of these are previously known lenses or lens candidates. We inspect a further 9428 candidates with a different score threshold, and identify four new candidates. We present 84 new strong lens candidates, selected after a few hours of visual inspection by astronomers. This catalogue contains a comparable number of high-redshift lenses to that predicted by simulations. Based on simulations, we estimate our sample to contain most discoverable lenses in this imaging and at this redshift range.