Recently,　small-scale　convolutional　neural　networks　(CNNs)　have　become　a　hot　research　topic　due　to　the　fewer　training　parameters　and　shorter　training　time,　while　their　accuracy　is　generally　degraded　compared　with　large-scale　CNNs.　To　this　end,　in　this　paper,　we　propose　a　small-scale　CNN　with　sparse　representation　(a　sparse　small-scale　CNN)　for　image　classification.　First,　the　Gabor　filter　is　a　representative　sparse　representation,　so　we　integrate　it　into　the　standard　AlexNet　to　establish　a　sparse　Gabor-AlexNet　architecture　to　better　extract　the　feature　of　images.　Second,　to　improve　further　the　performance　of　the　above　Gabor-AlexNet.,　a　learnable　Gabor-AlexNet　with　only　the　increase　of　a　few　learning　parameters　is　constructed　for　image　classification.　Finally,　we　test　the　Gabor-AlexNet　on　small-scale　datasets　including　Extended　Yale　B,　CASIA-FaceV5.,　Original　Brodatz　and,　DTD.　The　proposed　method　outperforms　the　standard　AlexNet　in　the　precision　and　speed　as　classification　benchmark.　Then,　our　learnable　Gabor-AlexNet　is　also　superior　to　the　Gabor-AlexNet　for　classification　performance　on　the　CIFAR-10　dataset.　©　2021　IEEE.