We constructed a far-ultraviolet (FUV) all-sky map based on observations from the Far Ultraviolet Imaging Spectrograph (FIMS) aboard the Korean microsatellite Science and Technology SATellite-1. For the ∼20 percent of the sky not covered by FIMS observations, predictions from a deep artificial neural network were used. Seven data sets were chosen for input parameters, including five all-sky maps of Hα, E(B ？ V), N(H？I), and two X-ray bands, with Galactic longitudes and latitudes. 70 percent of the pixels of the observed FIMS data set were randomly selected for training as target parameters and the remaining 30 percent were used for validation. A simple four-layer neural network architecture, which consisted of three convolution layers and a dense layer at the end, was adopted, with an individual activation function for each convolution layer; each convolution layer was followed by a dropout layer. The predicted FUV intensities exhibited good agreement with Galaxy Evolution Explorer observations made in a similar FUV wavelength band for high Galactic latitudes. As a sample application of the constructed map, a dust scattering simulation was conducted with model optical parameters and a Galactic dust model for a region that included observed and predicted pixels. Overall, FUV intensities in the observed and predicted regions were reproduced well.