Convolutional　neural　networks　(CNNs)　have　made　remarkable　success　in　image　classification.　However,　it　is　still　an　open　problem　how　to　develop　new　models　instead　of　CNNs.　Here,　we　propose　a　novel　model,　namely　two-dimensional　perceptron　(TDP),　to　get　direct　input　of　2D　data　for　further　processing.　A　TDP　computes　hidden　neurons　from　the　input　via　left/right　matrix　multiplication,　producing　left-weighted　TDP　and　right-weighted　TDP,　respectively.　Experimental　results　on　MNIST　and　COIL-20　datasets　show　that,　in　cases　with　the　same　number　of　hidden　neurons,　the　model　obtains　5%-45%　relative　performance　improvement　and　2　x-36x　speedup　in　comparison　with　the　corresponding　multilayer　perceptron　and　convolutional　neural　network.　Hence,　it　is　a　promising　and　potential　model　that　may　open　some　new　directions　for　deep　neural　networks,　particularly　alternatives　to　CNNs.