Fog　computing　is　promising　to　solve　the　challenge　caused　by　an　extremely　large　amount　of　data　on　cloud　computing.　In　this　study,　an　efficient　binary　convolutional　neural　network　with　numerous　skip　connections　(BNSC-Net)　is　proposed　for　fog　computing　to　enable　real-time　smart　industrial　applications.　This　network　features　decomposition　convolution　kernels　and　concatenated　feature　maps.　Moreover,　the　network　performance　is　further　improved　through　expanding　the　update　interval　of　the　straight-through　estimator.　To　verify　the　performance,　BNSC-Net　is　tested　on　two　broadly　used　public　data　sets:　1)　ImageNet　and　2)　CIFAR-10.　An　ablation　study　is　first　conducted　to　verify　the　effectiveness　of　the　proposed　improved　operations,　and　results　demonstrate　that　BNSC-Net　can　obviously　increase　the　classification　accuracy　for　both　data　sets.　ImageNet-based　classification　results　indicate　that　BNSC-Net　can　achieve　59.9%　TOP-1　accuracy　that　is　2.6%　higher　than　the　state-of-the-art　binary　neural　networks,　such　as　projection　convolutional　neural　networks　(PCNNs).　Finally,　a　subset　with　ten　classes　is　selected　from　ImageNet　to　simulate　the　data　collected　in　the　smart　industry　with　limited　categories,　based　on　which　BNSC-Net　also　demonstrates　an　impressive　classification　performance　with　friendly　memory　and　calculation　requirements.　Particularly,　the　receiver　operating　characteristic　curves　of　BNSC-Net　surpass　that　of　the　state-of-the-art　algorithm　DeepIns.　Therefore,　the　proposed　BNSC-Net　is　effective　and　efficient　for　building　deep　learning-enabled　industrial　applications　on　fog　nodes.