Artificial　neural　networks　(ANN)　which　include　deep　learning　neural　networks　(DNN)　have　problems　such　as　the　local　minimal　problem　of　Back　propagation　neural　network　(BPNN),　the　unstable　problem　of　Radial　basis　function　neural　network　(RBFNN)　and　the　limited　maximum　precision　problem　of　Convolutional　neural　network　(CNN).　Performance　(training　speed,　precision,　etc.)　of　BPNN,　RBFNN　and　CNN　are　expected　to　be　improved.　Main　works　are　as　follows:　Firstly,　based　on　existing　BPNN　and　RBFNN,　Wavelet　neural　network　(WNN)　is　implemented　in　order　to　get　better　performance　for　further　improving　CNN.　WNN　adopts　the　network　structure　of　BPNN　in　order　to　get　faster　training　speed.　WNN　adopts　the　wavelet　function　as　an　activation　function,　whose　form　is　similar　to　the　radial　basis　function　of　RBFNN,　in　order　to　solve　the　local　minimum　problem.　Secondly,　WNN-based　Convolutional　wavelet　neural　network　(CWNN)　method　is　proposed,　in　which　the　fully　connected　layers　(FCL)　of　CNN　is　replaced　by　WNN.　Thirdly,　comparative　simulations　based　on　MNIST　and　CIFAR-10　datasets　among　the　discussed　methods　of　BPNN,　RBFNN,　CNN　and　CWNN　are　implemented　and　analyzed.　Fourthly,　the　wavelet-based　Convolutional　Neural　Network　(WCNN)　is　proposed,　where　the　wavelet　transformation　is　adopted　as　the　activation　function　in　Convolutional　Pool　Neural　Network　(CPNN)　of　CNN.　Fifthly,　simulations　based　on　CWNN　are　implemented　and　analyzed　on　the　MNIST　dataset.　Effects　are　as　follows:　Firstly,　WNN　can　solve　the　problems　of　BPNN　and　RBFNN　and　have　better　performance.　Secondly,　the　proposed　CWNN　can　reduce　the　mean　square　error　and　the　error　rate　of　CNN,　which　means　CWNN　has　better　maximum　precision　than　CNN.　Thirdly,　the　proposed　WCNN　can　reduce　the　mean　square　error　and　the　error　rate　of　CWNN,　which　means　WCNN　has　better　maximum　precision　than　CWNN.