A new kind of stochastic web due to discontinuity was found in classical 1-dimensional kicked billiards model (1D-KBM),which is a discontinuous Hamiltonian system.Its classical diffusion characteristics have been discussed in our previous article.The quantum diffusion characteristics of 1D-KBM was studied,the interesting thing is that it was found to be related with the classical diffusion characteristics,and some more special characteristics for the quantum case were also pointed out,especially those present different properties forα[0,π/2) and α[-π/2,0).