We present a new sample of galaxy-scale strong gravitational lens candidates, selected from 904deg^2^ of Data Release 4 of the Kilo-Degree Survey, i.e. the 'Lenses in the Kilo-Degree Survey' (LinKS) sample. We apply two convolutional neural networks (ConvNets) to ~88000 colour-magnitude-selected luminous red galaxies yielding a list of 3500 strong lens candidates. This list is further downselected via human inspection. The resulting LinKS sample is composed of 1983 rank-ordered targets classified as 'potential lens candidates' by at least one inspector. Of these, a high-grade subsample of 89 targets is identified with potential strong lenses by all inspectors. Additionally, we present a collection of another 200 strong lens candidates discovered serendipitously from various previous ConvNet runs. A straightforward application of our procedure to future Euclid or Large Synoptic Survey Telescope data can select a sample of ~3000 lens candidates with less than 10 per cent expected false positives and requiring minimal human intervention.