The　adaptive　hinging　hyperplane　(AHH)　model　is　a　popular　piecewise　linear　representation　with　a　generalized　tree　structure　and　has　been　successfully　applied　in　dynamic　system　identification.　In　this　article,　we　aim　to　construct　the　deep　AHH　(DAHH)　model　to　extend　and　generalize　the　networking　of　AHH　model　for　high-dimensional　problems.　The　network　structure　of　DAHH　is　determined　through　a　forward　growth,　in　which　the　activity　ratio　is　introduced　to　select　effective　neurons　and　no　connecting　weights　are　involved　between　the　layers.　Then,　all　neurons　in　the　DAHH　network　can　be　flexibly　connected　to　the　output　in　a　skip-layer　format,　and　only　the　corresponding　weights　are　the　parameters　to　optimize.　With　such　a　network　framework,　the　backpropagation　algorithm　can　be　implemented　in　DAHH　to　efficiently　tackle　large-scale　problems　and　the　gradient　vanishing　problem　is　not　encountered　in　the　training　of　DAHH.　In　fact,　the　optimization　problem　of　DAHH　can　maintain　convexity　with　convex　loss　in　the　output　layer,　which　brings　natural　advantages　in　optimization.　Different　from　the　existing　neural　networks,　DAHH　is　easier　to　interpret,　where　neurons　are　connected　sparsely　and　analysis　of　variance　(ANOVA)　decomposition　can　be　applied,　facilitating　to　revealing　the　interactions　between　variables.　A　theoretical　analysis　toward　universal　approximation　ability　and　explicit　domain　partitions　are　also　derived.　Numerical　experiments　verify　the　effectiveness　of　the　proposed　DAHH.